Some results on the signed complete graphs

Volume 10, Issue 3 (11-2024) mmr 2024, 10(3): 18-32 | Back to browse issues page

Heydari F. Some results on the signed complete graphs. mmr 2024; 10 (3) :18-32
URL: http://mmr.khu.ac.ir/article-1-3339-en.html

Some results on the signed complete graphs

Farideh Heydari ^*

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran , f-heydari@kiau.ac.ir

Abstract: (114 Views)

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

. 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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