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Tytuł:
Decomposing 10-Regular Graphs into Paths of Length 5
Autorzy:
Xie, Mengmeng
Zhou, Chuixiang
Powiązania:
https://bibliotekanauki.pl/articles/32222554.pdf
Data publikacji:
2022-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
10-regular graph
decomposition
path
Opis:
Let G be a 10-regular graph which does not contain any 4-cycles. In this paper, we prove that G can be decomposed into paths of length 5, such that every vertex is a terminal of exactly two paths.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1089-1097
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of Regular Nut Graphs for Degree at Most 11
Autorzy:
Fowler, Patrick W.
Gauci, John Baptist
Goedgebeur, Jan
Pisanski, Tomaž
Sciriha, Irene
Powiązania:
https://bibliotekanauki.pl/articles/31550028.pdf
Data publikacji:
2020-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
nut graph
core graph
regular graph
nullity
Opis:
A nut graph is a singular graph with one-dimensional kernel and corresponding eigenvector with no zero elements. The problem of determining the orders n for which d-regular nut graphs exist was recently posed by Gauci, Pisanski and Sciriha. These orders are known for d ≤ 4. Here we solve the problem for all remaining cases d ≤ 11 and determine the complete lists of all d-regular nut graphs of order n for small values of d and n. The existence or non-existence of small regular nut graphs is determined by a computer search. The main tool is a construction that produces, for any d-regular nut graph of order n, another d-regular nut graph of order n+2d. If we are given a sufficient number of d-regular nut graphs of consecutive orders, called seed graphs, this construction may be applied in such a way that the existence of all d-regular nut graphs of higher orders is established. For even d the orders n are indeed consecutive, while for odd d the orders n are consecutive even numbers. Furthermore, necessary conditions for combinations of order and degree for vertex-transitive nut graphs are derived.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 2; 533-557
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Splitting Cubic Circle Graphs
Autorzy:
Traldi, Lorenzo
Powiązania:
https://bibliotekanauki.pl/articles/31340797.pdf
Data publikacji:
2016-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
circle graph
split decomposition
regular graph
Opis:
We show that every 3-regular circle graph has at least two pairs of twin vertices; consequently no such graph is prime with respect to the split decomposition. We also deduce that up to isomorphism, K4 and K3,3 are the only 3-connected, 3-regular circle graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 723-741
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Smallest Regular Graphs of Given Degree and Diameter
Autorzy:
Knor, Martin
Powiązania:
https://bibliotekanauki.pl/articles/30147224.pdf
Data publikacji:
2014-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
regular graph
degree/diameter problem
extremal graph
Opis:
In this note we present a sharp lower bound on the number of vertices in a regular graph of given degree and diameter.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 1; 187-191
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A reduction of the Graph Reconstruction Conjecture
Autorzy:
Monikandan, S.
Balakumar, J.
Powiązania:
https://bibliotekanauki.pl/articles/30148259.pdf
Data publikacji:
2014-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
reconstruction
diameter
geodetic graph
interval-regular graph
Opis:
A graph is said to be reconstructible if it is determined up to isomorphism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC) asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G) = 2 or diam(G) = diam(Ḡ) = 3 are reconstructible.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 3; 529-537
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kaleidoscopic Edge-Coloring of Complete Graphs and r-Regular Graphs
Autorzy:
Li, Xueliang
Zhu, Xiaoyu
Powiązania:
https://bibliotekanauki.pl/articles/31343197.pdf
Data publikacji:
2019-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
k -kaleidoscope
regular graph
edge-coloring
Opis:
For an $r$-regular graph $G$, we define an edge-coloring $c$ with colors from ${1, 2, . . ., k}$, in such a way that any vertex of $G$ is incident with at least one edge of each color. The multiset-color $c_m(v)$ of a vertex $v$ is defined as the ordered tuple $ (a_1, a_2, . . ., a_k) $, where $ a_i (1 \le i \le k) $ denotes the number of edges of color $i$ which are incident with $v$ in $G$. Then this edge-coloring $c$ is called a $k$-kaleidoscopic coloring of $G$ if every two distinct vertices in $G$ have different multiset-colors and in this way the graph $G$ is defined as a $k$-kaleidoscope. In this paper, we determine the integer $k$ for a complete graph $ K_n $ to be a $k$-kaleidoscope, and hence solve a conjecture in [P. Zhang, A Kaleidoscopic View of Graph Colorings, (Springer Briefs in Math., New York, 2016)] that for any integers $n$ and $k$ with $ n \ge k + 3 \ge 6 $, the complete graph $ K_n$ is a $k$-kaleidoscope. Then, we construct an $r$-regular 3-kaleidoscope of order \( \binom{r-1}{2} - 1 \) for each integer $ r \ge 7 $, where $ r \equiv 3 (mod 4) $, which solves another conjecture in [P. Zhang, A Kaleidoscopic View of Graph Colorings, (Springer Briefs in Math., New York, 2016)] on the maximum order of $r$-regular 3-kaleidoscopes.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 4; 881-888
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:
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:
Maximum Hypergraphs without Regular Subgraphs
Autorzy:
Kim, Jaehoon
Kostochka, Alexandr V.
Powiązania:
https://bibliotekanauki.pl/articles/30147226.pdf
Data publikacji:
2014-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypergraphs
set system
subgraph
regular graph
Opis:
We show that an n-vertex hypergraph with no r-regular subgraphs has at most $2^{n−1}+r−2$ edges. We conjecture that if n > r, then every n-vertex hypergraph with no r-regular subgraphs having the maximum number of edges contains a full star, that is, $2^{n−1}$ distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n > r cannot be weakened.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 1; 151-166
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Note on the Crossing Numbers of 5-Regular Graphs
Autorzy:
Ouyang, Zhangdong
Powiązania:
https://bibliotekanauki.pl/articles/31348107.pdf
Data publikacji:
2020-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
crossing number
5-regular graph
drawing
Opis:
The crossing number cr(G) of a graph G is the smallest number of edge crossings in any drawing of G. In this paper, we prove that there exists a unique 5-regular graph G on 10 vertices with cr(G) = 2. This answers a question by Chia and Gan in the negative. In addition, we also give a new proof of Chia and Gan’s result which states that if G is a non-planar 5-regular graph on 12 vertices, then cr(G) ≥ 2.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 4; 1127-1140
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Fisher-type inequalities for designs on regular graphs
O nierówności Fishera dla układów na grafach regularnych
Autorzy:
Mielniczuk, J.
Powiązania:
https://bibliotekanauki.pl/articles/9821.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Przyrodniczy w Lublinie. Katedra Zastosowań Matematyki i Informatyki
Tematy:
Fisher-type inequality
design
regular graph
graph theory
Źródło:
Colloquium Biometricum; 2008, 38
1896-7701
Pojawia się w:
Colloquium Biometricum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Minimum Number of Spanning Trees in Cubic Multigraphs
Autorzy:
Bogdanowicz, Zbigniew R.
Powiązania:
https://bibliotekanauki.pl/articles/32083837.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cubic multigraph
spanning tree
regular graph
enumeration
Opis:
Let G2n, H2n be two non-isomorphic connected cubic multigraphs of order 2n with parallel edges permitted but without loops. Let t(G2n), t (H2n) denote the number of spanning trees in G2n, H2n, respectively. We prove that for n ≥ 3 there is the unique G2n such that t(G2n) < t(H2n) for any H2n. Furthermore, we prove that such a graph has t(G2n) = 522n−3 spanning trees. Based on our results we give a conjecture for the unique r-regular connected graph H2n of order 2n and odd degree r that minimizes the number of spanning trees.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 149-159
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Spectra of Orders for k-Regular Graphs of Girth g
Autorzy:
Jajcay, Robert
Raiman, Tom
Powiązania:
https://bibliotekanauki.pl/articles/32222719.pdf
Data publikacji:
2021-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cage
k -regular graph
girth
Sauer bound
Opis:
A (k, g)-graph is a k-regular graph of girth g. Given k ≥ 2 and g ≥ 3, infinitely many (k, g)-graphs of infinitely many orders are known to exist. Our goal, for given k and g, is the classification of all orders n for which a (k, g)-graph of order n exists; we choose to call the set of all such orders the spectrum of orders of (k, g)-graphs. The smallest of these orders (the first element in the spectrum) is the order of a (k, g)-cage; the (k, g)-graph of the smallest possible order. The exact value of this order is unknown for the majority of parameters (k, g). We determine the spectra of orders for (2, g), g ≥ 3, (k, 3), k ≥ 2, and (3, 5)-graphs, as well as the spectra of orders of some families of (k, 4)-graphs. In addition, we present methods for obtaining (k, g)-graphs that are larger then the smallest known (k, g)-graphs, but are smaller than (k, g)-graphs obtained by Sauer. Our constructions start from (k, g)-graphs that satisfy specific conditions derived in this paper and result in graphs of orders larger than the original graphs by one or two vertices. We present theorems describing ways to obtain ‘starter graphs’ whose orders fall in the gap between the well-known Moore bound and the constructive bound derived by Sauer and are the first members of an infinite sequence of graphs whose orders cover all admissible orders larger than those of the ‘starter graphs’.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1115-1125
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Tree domatic number in graphs
Autorzy:
Chen, X. G.
Powiązania:
https://bibliotekanauki.pl/articles/255594.pdf
Data publikacji:
2007
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
tree domatic number
regular graph
planar graph
Cartesian product
Opis:
A dominating set S in a graph G is a tree dominating set of G if the subgraph induced by S is a tree. The tree domatic number of G is the maximum number of pairwise disjoint tree dominating sets in V(G). First, some exact values of and sharp bounds for the tree domatic number are given. Then, we establish a sharp lower bound for the number of edges in a connected graph of given order and given tree domatic number, and we characterize the extremal graphs. Finally, we show that a tree domatic number of a planar graph is at most 4 and give a characterization of planar graphs with the tree domatic number 3.
Źródło:
Opuscula Mathematica; 2007, 27, 1; 5-11
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Spectral Characterization of the S-Clique Extension of the Triangular Graphs
Autorzy:
Tan, Ying-Ying
Koolen, Jack H.
Xia, Zheng-Jiang
Powiązania:
https://bibliotekanauki.pl/articles/31564711.pdf
Data publikacji:
2020-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
co-edge-regular graph
triangular graph
s-clique extension
Opis:
A regular graph is co-edge regular if there exists a constant µ such that any two distinct and non-adjacent vertices have exactly µ common neighbors. In this paper, we show that for integers s ≥ 2 and n large enough, any co-edge-regular graph which is cospectral with the s-clique extension of the triangular graph T (n) is exactly the s-clique extension of the triangular graph T (n).
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 2; 663-676
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 30

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