The $ k $-${rm bf{ th}}$ spectral moment of signed complete graphs

Abstract

Let $Gamma=(G,sigma)$ be a signed graph, where $G$ is the underlying simple graph with at least one edge and $sigma : E(G) longrightarrow lbrace -,+rbrace$ is the sign function on the edges of $G$. In this paper, we study the $ k $-th spectral moment of $(K_n,sigma)$, for a signature $sigma$. Also, we obtain the number of negative cycles in a signed complete graph whose negative edges induce the disjoint union of two distinct complete bipartite graphs.