Results 21 to 30 of about 10,152,062 (308)
A Short Proof of the Size of Edge-Extremal Chordal Graphs
Journal of Mathematical Sciences and Modelling, 2022 [3] have recently determined the maximum number of edges of a chordal graph with a maximum degree less than $d$ and the matching number at most $\nu$ by exhibiting a family of chordal graphs achieving this bound. We provide simple proof of their result.
Mordechai Shalom
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Matching Number, Independence Number, and Covering Vertex Number of Γ(Zn)
Mathematics, 2019 Graph invariants are the properties of graphs that do not change under graph isomorphisms, the independent set decision problem, vertex covering problem, and matching number problem are known to be NP-Hard, and hence it is not believed that there are ...
Eman AbuHijleh +3 more
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Matching number and characteristic polynomial of a graph
Journal of Taibah University for Science, 2020 Matching number and the spectral properties depending on the characteristic polynomial of a graph obtained by means of the adjacency polynomial has many interesting applications in different areas of science.
Aysun Yurttas Gunes +3 more
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Discrete Mathematics, 1980 AbstractWe consider the Ramsey number r(sK2, G) where sK2(s⩾1) denotes a set of s disjoint edges and G is an arbitrary finite simple graph with no isolated vertices. We obtain upper and lower bounds in the general case. Exact results are obtained for certain classes of graphs.
Ralph J. Faudree +2 more
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, 2011 This article introduces the quantitative analysis of choice behavior by describing a number of equations developed over the years to describe the relation between the allocation of behavior under concurrent schedules of reinforcement and the consequences
Timothy L. Edwards +7 more
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The extremal graphs with respect to their nullity
Journal of Inequalities and Applications, 2016 The nullity of a graph G, denoted by η ( G ) $\eta(G)$ , is the multiplicity of the eigenvalue zero of its adjacency matrix. In this paper, we determine all graphs with η ( G ) = n ( G ) − 2 m ( G ) − c ( G ) $\eta(G)=n(G) - 2m(G) -c(G)$ , where c ( G ) =
Sa Rula, An Chang, Yirong Zheng
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Counterexamples to a conjecture on matching Kneser graphs [PDF]
Transactions on Combinatorics, 2023 Let $G$ be a graph and $r\in\mathbb{N}$. The matching Kneser graph $\textsf{KG}(G, rK_2)$ is a graph whose vertex set is the set of $r$-matchings in $G$ and two vertices are adjacent if their corresponding matchings are edge-disjoint. In [M. Alishahi and
Moharram N. Iradmusa
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On the Number of Group-Weighted Matchings [PDF]
Journal of Algebraic Combinatorics, 1998 Let \(G\) be a bipartite graph with bipartition \(\{A, B\}\), where \(| A| = | B| \). Let \(K\) be a finite abelian group with \(k\) elements, and let \(w : E(G) \rightarrow K\) be a weight assignment on the edges of \(G\). For a subset \(S\) of the edge set of \(G\), let \(w(S)\) denote the product of the weights of the edges in \(S\).
Kahn, Jeff, Meshulam, Roy
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Two Degree Distance Based Topological Indices of Chemical Trees
IEEE Access, 2019 Let G = (VG, EG) be a simple and connected graph. The eccentric connectivity index of G is represented as ξc(G) = Σx∈VG degG(x)ecG(x), where degG(x) and ecG(x) represent the degree and the eccentricity of x, respectively.
Shehnaz Akhter
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The difference and ratio of the fractional matching number and the matching number of graphs
Discrete Mathematics, 2016 Given a graph $G$, the matching number of $G$, written $α'(G)$, is the maximum size of a matching in $G$, and the fractional matching number of $G$, written $α'_f(G)$, is the maximum size of a fractional matching of $G$. In this paper, we prove that if $G$ is an $n$-vertex connected graph that is neither $K_1$ nor $K_3$, then $α'_f(G)-α'(G) \le \frac{n-
Ilkyoo Choi, Jaehoon Kim, Suil O
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