University of Guilan Journal of Algebra and Related Topics 2345-3931 7 1 2019 06 01 The $ k $-${\rm \bf{ th}}$ spectral moment of signed complete graphs 35 44 3690 10.22124/jart.2019.13670.1150 EN S. Dalvandi Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran F. Heydari Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran M. Maghasedi Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran Journal Article 2019 06 25 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. https://jart.guilan.ac.ir/article_3690_d67598716ecc8ae5483f54f2bc56eeb6.pdf