منابع مشابه
New Graphs of Finite Mutation Type
To a directed graph without loops or 2-cycles, we can associate a skew-symmetric matrix with integer entries. Mutations of such skew-symmetric matrices, and more generally skew-symmetrizable matrices, have been defined in the context of cluster algebras by Fomin and Zelevinsky. The mutation class of a graph Γ is the set of all isomorphism classes of graphs that can be obtained from Γ by a seque...
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Let G = (V,E) be a simple graph with exactly n vertices and m edges. The aim of this paper is a new method for investigating nontriviality of the automorphism group of graphs. To do this, we prove that if |E| >=[(n - 1)2/2] then |Aut(G)|>1 and |Aut(G)| is even number.
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Let G = (V, E) be a locally finite graph, Ω ⊂ V be a bounded open domain, ∆ be the usual graph Laplacian, and λ1(Ω) be the first eigenvalue of −∆ with respect to Dirichlet boundary condition. Using the mountain pass theorem of Ambrosette and Rabinowitz, We prove that if α < λ1(Ω), then for any p > 2, there exists a positive solution to −∆u − αu = |u| p−2u in Ω◦, u = 0 on ∂Ω, where Ω◦ and...
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Let $G$ be a finite non-abelian group with center $Z(G)$. The non-commuting graph of $G$ is a simple undirected graph whose vertex set is $Gsetminus Z(G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy ne yx$. In this paper, we compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups..
متن کاملRelative non-Normal Graphs of a Subgroup of Finite Groups
Let G be a finite group and H,K be two subgroups of G. We introduce the relative non-normal graph of K with respect to H , denoted by NH,K, which is a bipartite graph with vertex sets HHK and KNK(H) and two vertices x ∈ H HK and y ∈ K NK(H) are adjacent if xy / ∈ H, where HK =Tk∈K Hk and NK(H) = {k ∈ K : Hk = H}. We determined some numerical invariants and state that when this graph is planar or...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2008
ISSN: 1077-8926
DOI: 10.37236/863