Abstract
ABSTRACT Let G be a graph with vertex set and be an matrix whose -entry is the maximum number of internally edge-disjoint paths between and , if , and zero otherwise. Also, define , where D is a diagonal matrix whose i-th diagonal element is the number of edge-disjoint cycles containing , whose is a multiple of J−I. Among other results, we determine the spectrum and the energy of the matrix for an arbitrary bicyclic graph G.
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