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Tytuł:
Bipartite embedding of (p, q)-trees
Autorzy:
Orchel, B.
Powiązania:
https://bibliotekanauki.pl/articles/254921.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
bipartite graph
tree
embedding graph
Opis:
A bipartite graph G = (L, R; E) where V(G) = L ∪ R, |L| = p, |R| = q is called a (p, q)-tree if |E(G)| = p + q - 1 and G has no cycles. A bipartite graph G = (L, R; E) is a subgraph of a bipartite graph H = (L'. R'; E') if L ⊆ L', R ⊆ R' and E ⊆ E'. In this paper we present sufficient degree conditions for a bipartite graph to contain a (p, q)-tree.
Źródło:
Opuscula Mathematica; 2006, 26, 1; 119-125
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
2-placement of (p,q)-trees
Autorzy:
Orchel, Beata
Powiązania:
https://bibliotekanauki.pl/articles/743376.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
tree
bipartite graph
packing graph
Opis:
Let G = (L,R;E) be a bipartite graph such that V(G) = L∪R, |L| = p and |R| = q. G is called (p,q)-tree if G is connected and |E(G)| = p+q-1.
Let G = (L,R;E) and H = (L',R';E') be two (p,q)-tree. A bijection f:L ∪ R → L' ∪ R' is said to be a biplacement of G and H if f(L) = L' and f(x)f(y) ∉ E' for every edge xy of G. A biplacement of G and its copy is called 2-placement of G. A bipartite graph G is 2-placeable if G has a 2-placement. In this paper we give all (p,q)-trees which are not 2-placeable.
Źródło:
Discussiones Mathematicae Graph Theory; 2003, 23, 1; 23-36
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Arboreal structure and regular graphs of median-like classes
Autorzy:
Brešar, Bostjan
Powiązania:
https://bibliotekanauki.pl/articles/743403.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
median graph
tree
gatedness
amalgam
periphery
regular graph
Opis:
We consider classes of graphs that enjoy the following properties: they are closed for gated subgraphs, gated amalgamation and Cartesian products, and for any gated subgraph the inverse of the gate function maps vertices to gated subsets. We prove that any graph of such a class contains a peripheral subgraph which is a Cartesian product of two graphs: a gated subgraph of the graph and a prime graph minus a vertex. Therefore, these graphs admit a peripheral elimination procedure which is a generalization of analogous procedure in median graphs. We characterize regular graphs of these classes whenever they enjoy an additional property. As a corollary we derive that regular weakly median graphs are precisely Cartesian products in which each factor is a complete graph or a hyperoctahedron.
Źródło:
Discussiones Mathematicae Graph Theory; 2003, 23, 2; 215-225
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graphs that are Critical for the Packing Chromatic Number
Autorzy:
Brešar, Boštjan
Ferme, Jasmina
Powiązania:
https://bibliotekanauki.pl/articles/32318620.pdf
Data publikacji:
2022-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
packing coloring
critical graph
diameter
block graph
tree
Opis:
Given a graph G, a coloring c : V (G) → {1, …, k} such that c(u) = c(v) = i implies that vertices u and v are at distance greater than i, is called a packing coloring of G. The minimum number of colors in a packing coloring of G is called the packing chromatic number of G, and is denoted by χρ(G). In this paper, we propose the study of χρ-critical graphs, which are the graphs G such that for any proper subgraph H of G, χρ(H) < χρ(G). We characterize χρ-critical graphs with diameter 2, and χρ-critical block graphs with diameter 3. Furthermore, we characterize χρ-critical graphs with small packing chromatic number, and we also consider χρ-critical trees. In addition, we prove that for any graph G and every edge e ∈ E(G), we have (χρ(G)+1)/2 ≤ χρ(G−e) ≤ χρ(G), and provide a corresponding realization result, which shows that χρ(G − e) can achieve any of the integers between these bounds.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 2; 569-589
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On non-z(mod k) dominating sets
Autorzy:
Caro, Yair
Jacobson, Michael
Powiązania:
https://bibliotekanauki.pl/articles/743399.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
dominating set
tree
unicyclic graph
Opis:
For a graph G, a positive integer k, k ≥ 2, and a non-negative integer with z < k and z ≠ 1, a subset D of the vertex set V(G) is said to be a non-z (mod k) dominating set if D is a dominating set and for all x ∈ V(G), |N[x]∩D| ≢ z (mod k).For the case k = 2 and z = 0, it has been shown that these sets exist for all graphs. The problem for k ≥ 3 is unknown (the existence for even values of k and z = 0 follows from the k = 2 case.) It is the purpose of this paper to show that for k ≥ 3 and with z < k and z ≠ 1, that a non-z(mod k) dominating set exist for all trees. Also, it will be shown that for k ≥ 4, z ≥ 1, 2 or 3 that any unicyclic graph contains a non-z(mod k) dominating set. We also give a few special cases of other families of graphs for which these dominating sets must exist.
Źródło:
Discussiones Mathematicae Graph Theory; 2003, 23, 1; 189-199
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Trees as Star Complements in Regular Graphs
Autorzy:
Rowlinson, Peter
Powiązania:
https://bibliotekanauki.pl/articles/31562766.pdf
Data publikacji:
2020-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
eigenvalue
regular graph
star complement
tree
Opis:
Let G be a connected r-regular graph (r > 3) of order n with a tree of order t as a star complement for an eigenvalue µ ∉ {−1, 0}. It is shown that n ≤ 1/2 (r + 1)t − 2. Equality holds when G is the complement of the Clebsch graph (with µ = 1, r = 5, t = 6, n = 16).
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 2; 621-636
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Upper bounds on distance vertex irregularity strength of some families of graphs
Autorzy:
Cichacz, Sylwia
Görlich, Agnieszka
Semaničová-Feňovčíková, Andrea
Powiązania:
https://bibliotekanauki.pl/articles/2216229.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
distance vertex irregularity strength of a graph
hypercube
tree
graph
Opis:
For a graph G its distance vertex irregularity strength is the smallest integer k for which one can find a labeling f : V (G) → {1, 2, . . . , k} such that $ \sum_{x \in N(v)} f(x) \neq \sum_{x \in N(u)} f(x) $ for all vertices u, v of G, where N(v) is the open neighborhood of v. In this paper we present some upper bounds on distance vertex irregularity strength of general graphs. Moreover, we give upper bounds on distance vertex irregularity strength of hypercubes and trees.
Źródło:
Opuscula Mathematica; 2022, 42, 4; 561--571
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Statuses and double branch weights of quadrangular outerplanar graphs
Autorzy:
Bielak, Halina
Powroźnik, Kamil
Powiązania:
https://bibliotekanauki.pl/articles/747004.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Centroid
median
outerplanar graph
status
tree
Opis:
In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2015, 69, 1
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Maximal buttonings of trees
Autorzy:
Short, Ian
Powiązania:
https://bibliotekanauki.pl/articles/31232001.pdf
Data publikacji:
2014-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
centroid
graph metric
tree
walk
Wiener distance
Opis:
A buttoning of a tree that has vertices $v_1, v_2, . . ., v_n$ is a closed walk that starts at $v_1$ and travels along the shortest path in the tree to $v_2$, and then along the shortest path to $v_3$, and so forth, finishing with the shortest path from $v_n$ to $v_1$. Inspired by a problem about buttoning a shirt inefficiently, we determine the maximum length of buttonings of trees.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 2; 415-420
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Crossing Numbers of Products of Path with Graphs of Order Six
Autorzy:
Klešč, Marián
Petrillová, Jana
Powiązania:
https://bibliotekanauki.pl/articles/30146431.pdf
Data publikacji:
2013-07-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
drawing
crossing number
Cartesian product
path
tree
Opis:
The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. For the path $ P_n $ of length $ n $, the crossing numbers of Cartesian products $ G \square P_n $ for all connected graphs $G$ on five vertices are also known. In this paper, the crossing numbers of Cartesian products $ G \square P_n $ for graphs $ G $ of order six are studied. Let $ H $ denote the unique tree of order six with two vertices of degree three. The main contribution is that the crossing number of the Cartesian product $ H \square P_n $ is $ 2(n − 1) $. In addition, the crossing numbers of $ G \square P_n $ for fourty graphs $G$ on six vertices are collected.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 3; 571-582
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Trees with Distinguishing Index Equal Distinguishing Number Plus One
Autorzy:
Alikhani, Saeid
Klavžar, Sandi
Lehner, Florian
Soltani, Samaneh
Powiązania:
https://bibliotekanauki.pl/articles/31804165.pdf
Data publikacji:
2020-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
automorphism group
distinguishing index
distinguishing number
tree
unicyclic graph
Opis:
The distinguishing number (index) D(G) (D′ (G)) of a graph G is the least integer d such that G has an vertex (edge) labeling with d labels that is preserved only by the trivial automorphism. It is known that for every graph G we have D′ (G) ≤ D(G) + 1. In this note we characterize finite trees for which this inequality is sharp. We also show that if G is a connected unicyclic graph, then D′ (G) = D(G).
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 3; 875-884
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Conflict-Free Vertex-Connections of Graphs
Autorzy:
Li, Xueliang
Zhang, Yingying
Zhu, Xiaoyu
Mao, Yaping
Zhao, Haixing
Jendrol’, Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/31868621.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
vertex-coloring
conflict-free vertex-connection
2-connected graph
tree
Opis:
A path in a vertex-colored graph is called conflict-free if there is a color used on exactly one of its vertices. A vertex-colored graph is said to be conflict-free vertex-connected if any two vertices of the graph are connected by a conflict-free path. This paper investigates the question: for a connected graph G, what is the smallest number of colors needed in a vertex-coloring of G in order to make G conflict-free vertex-connected. As a result, we get that the answer is easy for 2-connected graphs, and very difficult for connected graphs with more cut-vertices, including trees.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 51-65
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Total connected domination game
Autorzy:
Bujtás, Csilla
Henning, Michael A.
Iršič, Vesna
Klavžar, Sandi
Powiązania:
https://bibliotekanauki.pl/articles/2050904.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
connected domination game
total connected domination game
graph product
tree
Opis:
The (total) connected domination game on a graph $G$ is played by two players, Dominator and Staller, according to the standard (total) domination game with the additional requirement that at each stage of the game the selected vertices induce a connected subgraph of $G$. If Dominator starts the game and both players play optimally, then the number of vertices selected during the game is the (total) connected game domination number $(\gamma_{tcg}(G))(\gamma_{cg(G)})$ of $G$. We show that $\gamma_{tcg}(G) \in \{\gamma_{cg}(G), \gamma_{cg}(G)+1, \gamma_{cg}(G)+2\}$, and consequently define $G$ as Class $i$ if $\gamma_{tcg}(G) = \gamma_{cg}(G)+i$ for $i \in \{0, 1, 2\}$. A large family of Class 0 graphs is constructed which contains all connected Cartesian product graphs and connected direct product graphs with minimum degree at least 2. We show that no tree is Class 2 and characterize Class 1 trees. We provide an infinite family of Class 2 bipartite graphs.
Źródło:
Opuscula Mathematica; 2021, 41, 4; 453-464
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Conflict-Free Connections of Graphs
Autorzy:
Czap, Július
Jendroľ, Stanislav
Valiska, Juraj
Powiązania:
https://bibliotekanauki.pl/articles/31342254.pdf
Data publikacji:
2018-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge-coloring
conflict-free connection
2-edge-connected graph
tree
Opis:
An edge-colored graph G is conflict-free connected if any two of its vertices are connected by a path, which contains a color used on exactly one of its edges. In this paper the question for the smallest number of colors needed for a coloring of edges of G in order to make it conflict-free connected is investigated. We show that the answer is easy for 2-edge-connected graphs and very difficult for other connected graphs, including trees.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 4; 911-920
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Total edge irregularity strength of trees
Autorzy:
Ivančo, Jaroslav
Jendrol', Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/743612.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph labelling
tree
irregularity strength
total labellings
total edge irregularity strength
Opis:
A total edge-irregular k-labelling ξ:V(G)∪ E(G) → {1,2,...,k} of a graph G is a labelling of vertices and edges of G in such a way that for any different edges e and f their weights wt(e) and wt(f) are distinct. The weight wt(e) of an edge e = xy is the sum of the labels of vertices x and y and the label of the edge e. The minimum k for which a graph G has a total edge-irregular k-labelling is called the total edge irregularity strength of G, tes(G). In this paper we prove that for every tree T of maximum degree Δ on p vertices
tes(T) = max{⎡(p+1)/3⎤,⎡(Δ+1)/2⎤}.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 3; 449-456
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 17

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