Ana Diánez

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For a connected graph G, the r-th extraconnectivity κr(G) is defined as the minimum cardinality of a cutset X such that all remaining components after the deletion of the vertices of X have at least r+1 vertices. The standard connectivity and superconnectivity correspond to κ0(G) and κ1(G), respectively. The minimum r-tree degree of G, denoted by ξr(G), is(More)
Let EX (ν; {C3, . . . ,Cn}) denote the set of graphs G of order ν that contain no cycles of length less than or equal to n which have maximum number of edges. In this paper we consider a problem posed by several authors: does G contain an n + 1 cycle? We prove that the diameter of G is at most n − 1, and present several results concerning the above(More)