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CORR
2010
Springer
14 years 11 months ago
2010
Springer
In an undirected graph G = (V, E), a subset C V such that C is a dominating set of G, and each vertex in V is dominated by a distinct subset of vertices from C, is called an iden...
CORR
2010
Springer
14 years 10 months ago
2010
Springer
Let G = (V, E) be a graph. Let c : V → N be a vertex-coloring of the vertices of G. For any vertex u, we denote by N[u] its closed neighborhood (u and its adjacent vertices), an...
JGT
2007
14 years 11 months ago
2007
It is known that for every integer k ≥ 4, each k-map graph with n vertices has at most kn − 2k edges. Previously, it was open whether this bound is tight or not. We show that ...
COMBINATORICS
2006
14 years 11 months ago
2006
A set of vertices S is a determining set for a graph G if every automorphism of G is uniquely determined by its action on S. The determining number of a graph is the size of a sma...
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CORR
2007
Springer
14 years 11 months ago
2007
Springer
For a given connected graph G on n vertices and m edges, we prove that its independence number α(G) is at least ((2m+n+2) -((2m+n+2)2 -16n2 )½ )/8. Keywords : independence numbe...