منابع مشابه
Inverse degree and edge-connectivity
Let G be a connected graph with vertex set V (G), order n = |V (G)|, minimum degree δ and edge-connectivity λ. Define the inverse degree of G as R(G) = ∑ v∈V (G) 1 d(v) , where d(v) denotes the degree of the vertex v. We show that if R(G) < 2 + 2 δ(δ + 1) + n− 2δ (n− δ − 2)(n− δ − 1) , then λ = δ. We also give an analogous result for triangle-free graphs.
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Let G be a finite connected graph. The degree distance D′(G) of G is defined as ∑ {u,v}⊆V (G)(deg u + deg v) dG(u, v), where degw is the degree of vertex w and dG(u, v) denotes the distance between u and v in G. In this paper, we give asymptotically sharp upper bounds on the degree distance in terms of order and edge-connectivity.
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For a connected graphG= (V ,E), an edge set S ⊂ E is a k-restricted-edge-cut, ifG−S is disconnected and every component of G− S has at least k vertices. The k-restricted-edge-connectivity of G, denoted by k(G), is defined as the cardinality of a minimum k-restricted-edge-cut. The k-isoperimetric-edge-connectivity is defined as k(G)=min{|[U,U ]| : U ⊂ V, |U | k, |U | k}, where [U,U ] is the set ...
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The power graph of a group G is the graph whose vertex set is G and two distinct vertices are adjacent if one is a power of the other. In this paper, the minimum degree of power graphs of certain classes of cyclic groups, abelian p-groups, dihedral groups and dicyclic groups are obtained. It is ascertained that the edge-connectivity and minimum degree of power graphs are equal, and consequently...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.06.041