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

Document Type: Research Paper


Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran


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.