The maximum index of signed complete graphs whose negative edges induce a bicyclic graph

2024/09/03 by Ziyi Fang, Fan Chen, Fang, Ziyi +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2409.01923

openalex publication_date 2024/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Γ=(K_n,H) be a signed complete graph whose negative edges induce a subgraph H. Let A(Γ) be the adjacency matrix of the signed graph Γ. The largest eigenvalue of A(Γ) is called the index of Γ. In this paper, the index of all the signed complete graphs whose negative edges induce a bicyclic graph B is investigated. Specifically, the structure of the bicyclic graph B such that Γ=(K_n,B) has the maximum index is determined.

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