Results 21 to 30 of about 8,766 (207)
, 2023 We introduce the notion of clique number of a tournament and investigate its relation with the dichromatic number. In particular, it permits defining $\dic$-bounded classes of tournaments, which is the paper's main topic.
Aboulker, Pierre +3 more
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On graphs with equal coprime index and clique number
AKCE International Journal of Graphs and Combinatorics, 2023 Recently, Katre et al. introduced the concept of the coprime index of a graph. They asked to characterize the graphs for which the coprime index is the same as the clique number. In this paper, we partially solve this problem.
Chetan Patil +2 more
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On the Planarity of Graphs Associated with Symmetric and Pseudo Symmetric Numerical Semigroups
Mathematics, 2023 Let S(m,e) be a class of numerical semigroups with multiplicity m and embedding dimension e. We call a graph GS an S(m,e)-graph if there exists a numerical semigroup S∈S(m,e) with V(GS)={x:x∈g(S)} and E(GS)={xy⇔x+y∈S}, where g(S) denotes the gap set of S.
Yongsheng Rao +4 more
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On annihilator graph of a finite commutative ring [PDF]
Transactions on Combinatorics, 2017 The annihilator graph $AG(R)$ of a commutative ring $R$ is a simple undirected graph with the vertex set $Z(R)^*$ and two distinct vertices are adjacent if and only if $ann(x) cup ann(y)$ $ neq $ $ann(xy)$.
Sanghita Dutta, Chanlemki Lanong
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Clique Search in Graphs of Special Class and Job Shop Scheduling
Mathematics, 2022 In this paper, we single out the following particular case of the clique search problem. The vertices of the given graph are legally colored with k colors and we are looking for a clique with k nodes in the graph.
Sándor Szabó, Bogdán Zaválnij
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Inverse Clique Domination in Graphs
Recoletos Multidisciplinary Research Journal, 2016 Let G be a connected simple graph. A nonempty subset S of the vertex set V (G) is a clique in G if the graph induced by S is complete. A clique S in G is a clique dominating set if it is a dominating set.
Carmelita Loquias +2 more
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Local and Global Clique Numbers
Journal of Combinatorial Theory, Series B, 1994 A graph \(G\) is said to have the \((p,q)\)-property for some integers \(p\geq q\geq 2\) if for every \(p\)-set of its vertices the induced subgraph contains a \(q\)-clique. The aim of the paper is to investigate relations of the type \((p,q)\to (n,s)\), meaning that each graph having the \((p,q)\)- property also has the \((n,s)\)-property.
Linial, N., Rabinovich, Y.
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Connected Domination Number and a New Invariant in Graphs with Independence Number Three [PDF]
Computer Science Journal of Moldova, 2021 Adding a connected dominating set of vertices to a graph $G$ increases its number of Hadwiger $h(G)$. Based on this obvious property in [2] we introduced a new invariant $\eta(G)$ for which $\eta(G)\leq h(G)$. We continue to study its property.
Vladimir Bercov
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On a class of polynomials associated with the Cliques in a graph and its applications
International Journal of Mathematics and Mathematical Sciences, 1989 The clique polynomial of a graph is defined. An explicit formula is then derived for the clique polynomial of the complete graph. A fundamental theorem and a reduction process is then given for clique polynomials.
E. J. Farrell
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Hard optimization problems have soft edges
Scientific Reports, 2023 Finding a Maximum Clique is a classic property test from graph theory; find any one of the largest complete subgraphs in an Erdös-Rényi G(N, p) random graph. We use Maximum Clique to explore the structure of the problem as a function of N, the graph size,
Raffaele Marino, Scott Kirkpatrick
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