Abstract
The distance energy of a connected graph [Formula: see text] is the sum of absolute values of the eigenvalues of the distance matrix of [Formula: see text]. In this paper, we study how the distance energy of the complete split graph [Formula: see text] changes when an edge is deleted from it. The complete split graph [Formula: see text] consists of a clique on [Formula: see text] vertices and an independent set on [Formula: see text] vertices in which each vertex of the clique is adjacent to each vertex of the independent set. We prove that the distance energy of the complete split graph [Formula: see text] always increases when an edge is deleted from it.
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