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Wyświetlanie 1-15 z 17
Tytuł:
On graphs with a unique minimum hull set
Autorzy:
Chartrand, Gary
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/743417.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
geodetic set
geodetic number
convex hull
hull set
hull number
hull graph
Opis:
We show that for every integer k ≥ 2 and every k graphs G₁,G₂,...,Gₖ, there exists a hull graph with k hull vertices v₁,v₂,...,vₖ such that link $L(v_i) = G_i$ for 1 ≤ i ≤ k. Moreover, every pair a, b of integers with 2 ≤ a ≤ b is realizable as the hull number and geodetic number (or upper geodetic number) of a hull graph. We also show that every pair a,b of integers with a ≥ 2 and b ≥ 0 is realizable as the hull number and forcing geodetic number of a hull graph.
Źródło:
Discussiones Mathematicae Graph Theory; 2001, 21, 1; 31-42
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The forcing geodetic number of a graph
Autorzy:
Chartrand, Gary
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/744241.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
geodetic set
geodetic number
forcing geodetic number
Opis:
For two vertices u and v of a graph G, the set I(u, v) consists of all vertices lying on some u-v geodesic in G. If S is a set of vertices of G, then I(S) is the union of all sets I(u,v) for u, v ∈ S. A set S is a geodetic set if I(S) = V(G). A minimum geodetic set is a geodetic set of minimum cardinality and this cardinality is the geodetic number g(G). A subset T of a minimum geodetic set S is called a forcing subset for S if S is the unique minimum geodetic set containing T. The forcing geodetic number $f_G(S)$ of S is the minimum cardinality among the forcing subsets of S, and the forcing geodetic number f(G) of G is the minimum forcing geodetic number among all minimum geodetic sets of G. The forcing geodetic numbers of several classes of graphs are determined. For every graph G, f(G) ≤ g(G). It is shown that for all integers a, b with 0 ≤ a ≤ b, a connected graph G such that f(G) = a and g(G) = b exists if and only if (a,b) ∉ {(1,1),(2,2)}.
Źródło:
Discussiones Mathematicae Graph Theory; 1999, 19, 1; 45-58
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Radio k-colorings of paths
Autorzy:
Chartrand, Gary
Nebeský, Ladislav
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/743194.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
radio k-coloring
radio k-chromatic number
Opis:
For a connected graph G of diameter d and an integer k with 1 ≤ k ≤ d, a radio k-coloring of G is an assignment c of colors (positive integers) to the vertices of G such that
d(u,v) + |c(u)- c(v)| ≥ 1 + k
for every two distinct vertices u and v of G, where d(u,v) is the distance between u and v. The value rcₖ(c) of a radio k-coloring c of G is the maximum color assigned to a vertex of G. The radio k-chromatic number rcₖ(G) of G is the minimum value of rcₖ(c) taken over all radio k-colorings c of G. In this paper, radio k-colorings of paths are studied. For the path Pₙ of order n ≥ 9 and n odd, a new improved bound for $rc_{n- 2}(Pₙ)$ is presented. For n ≥ 4, it is shown that
$rc_{n-3}(Pₙ) ≤ \binom{n-2} {2}$
Upper and lower bounds are also presented for rcₖ(Pₙ) in terms of k when 1 ≤ k ≤ n- 1. The upper bound is shown to be sharp when 1 ≤ k ≤ 4 and n is sufficiently large.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 1; 5-21
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Geodetic sets in graphs
Autorzy:
Chartrand, Gary
Harary, Frank
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/743733.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
geodetic set
geodetic number
upper geodetic number
Opis:
For two vertices u and v of a graph G, the closed interval I[u,v] consists of u, v, and all vertices lying in some u-v geodesic in G. If S is a set of vertices of G, then I[S] is the union of all sets I[u,v] for u, v ∈ S. If I[S] = V(G), then S is a geodetic set for G. The geodetic number g(G) is the minimum cardinality of a geodetic set. A set S of vertices in a graph G is uniform if the distance between every two distinct vertices of S is the same fixed number. A geodetic set is essential if for every two distinct vertices u,v ∈ S, there exists a third vertex w of G that lies in some u-v geodesic but in no x-y geodesic for x, y ∈ S and {x,y} ≠ {u,v}. It is shown that for every integer k ≥ 2, there exists a connected graph G with g(G) = k which contains a uniform, essential minimum geodetic set. A minimal geodetic set S has no proper subset which is a geodetic set. The maximum cardinality of a minimal geodetic set is the upper geodetic number g⁺(G). It is shown that every two integers a and b with 2 ≤ a ≤ b are realizable as the geodetic and upper geodetic numbers, respectively, of some graph and when a < b the minimum order of such a graph is b+2.
Źródło:
Discussiones Mathematicae Graph Theory; 2000, 20, 1; 129-138
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kaleidoscopic Colorings of Graphs
Autorzy:
Chartrand, Gary
English, Sean
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/31341692.pdf
Data publikacji:
2017-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge coloring
vertex coloring
kaleidoscopic coloring
kaleidoscope
Opis:
For an $r$-regular graph $G$, let $ c : E(G) \rightarrow [k] = {1, 2, . . ., k}$, $ k \ge 3 $, be an edge coloring of $G$, where every vertex of $G$ is incident with at least one edge of each color. For a vertex $v$ of $G$, the multiset-color $ c_m(v)$ of $v$ is defined as the ordered $k$-tuple $ (a_1, a_2, . . ., a_k) $ or $ a_1a_2…a_k$, where $a_i$ $(1 \le i \le k)$ is the number of edges in $G$ colored $i$ that are incident with $v$. The edge coloring $c$ is called $k$-kaleidoscopic if $ c_m(u) \ne c_m(v)$ for every two distinct vertices $u$ and $v$ of $G$. A regular graph $G$ is called a $k$-kaleidoscope if $G$ has a $k$-kaleidoscopic coloring. It is shown that for each integer $k \ge 3 $, the complete graph $ K_{k+3}$ is a $k$-kaleidoscope and the complete graph $ K_n $ is a 3-kaleidoscope for each integer $ n \ge 6 $. The largest order of an $r$-regular 3-kaleidoscope is \( \binom{r-1}{2} \). It is shown that for each integer $ r \ge 5 $ such that \( r \not\equiv 3 (\text{mod } 4) \), there exists an $r$-regular 3-kaleidoscope of order \( \binom{r-1}{2} \).
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 3; 711-727
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Another View of Bipartite Ramsey Numbers
Autorzy:
Bi, Zhenming
Chartrand, Gary
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/31342309.pdf
Data publikacji:
2018-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Ramsey number
bipartite Ramsey number
s -bipartite Ramsey number
Opis:
For bipartite graphs F and H and a positive integer s, the s-bipartite Ramsey number BRs(F,H) of F and H is the smallest integer t with t ≥ s such that every red-blue coloring of Ks,t results in a red F or a blue H. We evaluate this number for all positive integers s when F = K2,2 and H ∈ {K2,3,K3,3}.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 2; 587-605
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Distance defined by spanning trees in graphs
Autorzy:
Chartrand, Gary
Nebeský, Ladislav
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/743431.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
distance
geodesic
T-path
T-geodesic
T-distance
Opis:
For a spanning tree T in a nontrivial connected graph G and for vertices u and v in G, there exists a unique u-v path u = u₀, u₁, u₂,..., uₖ = v in T. A u-v T-path in G is a u- v path u = v₀, v₁,...,vₗ = v in G that is a subsequence of the sequence u = u₀, u₁, u₂,..., uₖ = v. A u-v T-path of minimum length is a u-v T-geodesic in G. The T-distance $d_{G|T}(u,v)$ from u to v in G is the length of a u-v T-geodesic. Let geo(G) and geo(G|T) be the set of geodesics and the set of T-geodesics respectively in G. Necessary and sufficient conditions are established for (1) geo(G) = geo(G|T) and (2) geo(G|T) = geo(G|T*), where T and T* are two spanning trees of G. It is shown for a connected graph G that geo(G|T) = geo(G) for every spanning tree T of G if and only if G is a block graph. For a spanning tree T of a connected graph G, it is also shown that geo(G|T) satisfies seven of the eight axioms of the characterization of geo(G). Furthermore, we study the relationship between the distance d and T-distance $d_{G|T}$ in graphs and present several realization results on parameters and subgraphs defined by these two distances.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 3; 485-506
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Rotation and jump distances between graphs
Autorzy:
Chartrand, Gary
Gavlas, Heather
Hevia, Héctor
Johnson, Mark
Powiązania:
https://bibliotekanauki.pl/articles/972022.pdf
Data publikacji:
1997
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge rotation
rotation distance
edge jump
jump distance
jump distance graph
Opis:
A graph H is obtained from a graph G by an edge rotation if G contains three distinct vertices u,v, and w such that uv ∈ E(G), uw ∉ E(G), and H = G-uv+uw. A graph H is obtained from a graph G by an edge jump if G contains four distinct vertices u,v,w, and x such that uv ∈ E(G), wx∉ E(G), and H = G-uv+wx. If a graph H is obtained from a graph G by a sequence of edge jumps, then G is said to be j-transformed into H. It is shown that for every two graphs G and H of the same order (at least 5) and same size, G can be j-transformed into H. For every two graphs G and H of the same order and same size, the jump distance $d_j(G,H)$ between G and H is defined as the minimum number of edge jumps required to j-transform G into H. The rotation distance $d_r(G,H)$ between two graphs G and H of the same order and same size is the minimum number of edge rotations needed to transform G into H. The jump and rotation distances of two graphs of the same order and same size are compared. For a set S of graphs of a fixed order at least 5 and fixed size, the jump distance graph $D_j(S)$ of S has S as its vertex set and where G₁ and G₂ in S are adjacent if and only if $d_j(G₁,G₂) = 1$. A graph G is a jump distance graph if there exists a set S of graphs of the same order and same size with $D_j(S) = G$. Several graphs are shown to be jump distance graphs, including all complete graphs, trees, cycles, and cartesian products of jump distance graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 1997, 17, 2; 285-300
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Full domination in graphs
Autorzy:
Brigham, Robert
Chartrand, Gary
Dutton, Ronald
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/743419.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
full domination
full star domination
full closed domination
full open domination
Opis:
For each vertex v in a graph G, let there be associated a subgraph $H_v$ of G. The vertex v is said to dominate $H_v$ as well as dominate each vertex and edge of $H_v$. A set S of vertices of G is called a full dominating set if every vertex of G is dominated by some vertex of S, as is every edge of G. The minimum cardinality of a full dominating set of G is its full domination number $γ_{FH}(G)$. A full dominating set of G of cardinality $γ_{FH}(G)$ is called a $γ_{FH}$-set of G. We study three types of full domination in graphs: full star domination, where $H_v$ is the maximum star centered at v, full closed domination, where $H_v$ is the subgraph induced by the closed neighborhood of v, and full open domination, where $H_v$ is the subgraph induced by the open neighborhood of v.
Źródło:
Discussiones Mathematicae Graph Theory; 2001, 21, 1; 43-62
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The set chromatic number of a graph
Autorzy:
Chartrand, Gary
Okamoto, Futaba
Rasmussen, Craig
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/744459.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
neighbor-distinguishing coloring
set coloring
neighborhood color set
Opis:
For a nontrivial connected graph G, let c: V(G)→ N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v of G, the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) ≠ NC(v) for every pair u,v of adjacent vertices of G. The minimum number of colors required of such a coloring is called the set chromatic number χₛ(G) of G. The set chromatic numbers of some well-known classes of graphs are determined and several bounds are established for the set chromatic number of a graph in terms of other graphical parameters.
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 3; 545-561
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Recognizable colorings of graphs
Autorzy:
Chartrand, Gary
Lesniak, Linda
VanderJagt, Donald
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/743507.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
recognizable coloring
recognition number
Opis:
Let G be a connected graph and let c:V(G) → {1,2,...,k} be a coloring of the vertices of G for some positive integer k (where adjacent vertices may be colored the same). The color code of a vertex v of G (with respect to c) is the ordered (k+1)-tuple code(v) = (a₀,a₁,...,aₖ) where a₀ is the color assigned to v and for 1 ≤ i ≤ k, $a_i$ is the number of vertices adjacent to v that are colored i. The coloring c is called recognizable if distinct vertices have distinct color codes and the recognition number rn(G) of G is the minimum positive integer k for which G has a recognizable k-coloring. Recognition numbers of complete multipartite graphs are determined and characterizations of connected graphs of order n having recognition numbers n or n-1 are established. It is shown that for each pair k,n of integers with 2 ≤ k ≤ n, there exists a connected graph of order n having recognition number k. Recognition numbers of cycles, paths, and trees are investigated.
Źródło:
Discussiones Mathematicae Graph Theory; 2008, 28, 1; 35-57
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 17

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