On the Multiplicity of -1 and 1 in Signed Complete Graphs

Abstract

Let r = (G, o) be a signed graph, where G is the underlying simple graph and a : E(G) -► {-,+} is the sign function on the edges of G. The adjacency matrix of a signed graph has - 1 or +1 for adjacent vertices, depending on the sign of the connecting edges. In this paper, we study the multiplicity of eigenvalues -1 and 1 for the signed complete graphs. Also, we determine the characteristic polynomial of a signed complete graph whose negative edges induce a complete tripartite graph. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.