Results 41 to 50 of about 8,766 (207)
An upper bound for the clique number using clique ceiling numbers
, 2019 In this article we present the idea of clique ceiling numbers of the vertices of a given graph that has a universal vertex. We follow up with a polynomial-time algorithm to compute an upper bound for the clique number of such a graph using clique ceiling numbers. We compare this algorithm with some upper bound formulas for the clique number.
Dharmarajan, R., Ramachandran, D.
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Comments on the Clique Number of Zero-Divisor Graphs of Zn
Journal of Mathematics, 2022 In 2008, J. Skowronek-kazio´w extended the study of the clique number ωGZn to the zero-divisor graph of the ring Zn, but their result was imperfect. In this paper, we reconsider ωGZn of the ring Zn and give some counterexamples. We propose a constructive
Yanzhao Tian, Lixiang Li
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Saturation numbers for Berge cliques
European Journal of Combinatorics16 pages, 1 ...
English, Sean +3 more
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A Different Short Proof of Brooks’ Theorem
Discussiones Mathematicae Graph Theory, 2014 Lovász gave a short proof of Brooks’ theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case.
Rabern Landon
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Prime ideal graphs of commutative rings
Indonesian Journal of Combinatorics, 2022 Let R be a finite commutative ring with identity and P be a prime ideal of R. The vertex set is R - {0} and two distinct vertices are adjacent if their product in P. This graph is called the prime ideal graph of R and denoted by ΓP.
Haval Mohammed Salih, Asaad A. Jund
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On General Reduced Second Zagreb Index of Graphs
Mathematics, 2022 Graph-based molecular structure descriptors (often called “topological indices”) are useful for modeling the physical and chemical properties of molecules, designing pharmacologically active compounds, detecting environmentally hazardous substances, etc.
Lkhagva Buyantogtokh +2 more
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Ideal based graph structures for commutative rings
Cubo, 2022 We introduce a graph structure $\gamrr$ for commutative rings with unity. We study some of the properties of the graph $\gamrr$. Also we study some parameters of $\gamrr$ and find rings for which $\gamrr$ is split.
M. I. Jinnah, Shine C. Mathew
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Lower bounds on the signed (total) $k$-domination number depending on the clique number
Communications in Combinatorics and Optimization, 2018 Let $G$ be a graph with vertex set $V(G)$. For any integer $k\ge 1$, a signed (total) $k$-dominating function is a function $f: V(G) \rightarrow \{ -1, 1\}$ satisfying $\sum_{x\in N[v]}f(x)\ge k$ ($\sum_{x\in N(v)}f(x)\ge k$) for every $v ...
L. Volkmann
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On oriented relative clique number
Electronic Notes in Discrete Mathematics, 2015 An oriented graph is a directed graph with no cycle of length one or two. The relative clique number of an oriented graph is the order of a largest subset X of vertices such that each pair of vertices are either adjacent or connected by a directed 2-path. It is known that the oriented relative clique number of a planar graph is at most 80.
Sandip Das, Swathyprabhu Mj, Sagnik Sen
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Forcing clique immersions through chromatic number [PDF]
Electronic Notes in Discrete Mathematics, 2016 Building on recent work of Dvo k and Yepremyan, we show that every simple graph of minimum degree $7t+7$ contains $K_t$ as an immersion and that every graph with chromatic number at least $3.54t + 4$ contains $K_t$ as an immersion. We also show that every graph on $n$ vertices with no stable set of size three contains $K_{2\lfloor n/5 \rfloor}$ as ...
Gauthier G., Le T. -N., Wollan P.
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