Some results on the signed complete graphs

Author
Farideh Heydari
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Abstract
Let be a signed complete graph of order whose negative edges induce a subgraph . If is a disjoint :union: of two graphs and , then we denote by . Let be the adjacency matrix of . The characteristic polynomial and eigenvalues of are called the characteristic polynomial and eigenvalues of , respectively. The index of is the largest eigenvalue of . In this paper, we study the characteristic polynomial of where is the disjoint :union: of complete graphs and is an arbitrary subgraph of Also, we compute the characteristic polynomial of for some classes of cactus graphs and provide a sharp bound for the index of .
Keywords
Index
characteristic polynomial
Signed graph
Complete graph
Cactus
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