Abstract
ABSTRACT In this paper, we study spectral properties of complex weighted digraphs. We show that a complex weighted digraph D is balanced if and only if D and have the same spectrum, where is the absolute value weighted digraph of D, that is, the digraph obtained by replacing the weight of each arc by its absolute value. We extend the concept of real energy to complex weighted digraphs and obtain extremal energy unicyclic complex weighted digraphs with cycle-weight in the punctured disk . We consider a family of complex weighted digraphs , in which each digraph has order n and cycles of length only with constant complex weight . We show that for each , the real energy of D is related to the real energy of unweighted cycle of length h and in some special cases real energy can be compared using quasi-order relation on coefficients of the characteristic polynomial. Finally, we obtain upper bounds on the real energy which generalize those known for unweighted digraphs and signed digraphs.
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