Abstract
A complex unit gain graph is a triple (or for short) consisting of a simple graph G, as the underlying graph of , the set of unit complex numbers and a gain function such that . Let be the adjacency matrix of . In this paper, we prove that where , , and are the number of positive eigenvalues of , the number of negative eigenvalues of , the matching number and the cyclomatic number of G, respectively. Furthermore, we characterize the graphs which attain the upper bounds and the lower bounds, respectively.
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