On the maximum A_α-spectral radius of unicyclic and bicyclic graphs with fixed girth or fixed number of pendant vertices

2023/11/22 by Joyentanuj Das, Das, Joyentanuj, Iswar Mahato +1
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2311.13364

openalex publication_date 2023/11/22 · openalex created_date 2023/11/24 · openalex updated_date 2026/07/28

Abstract

For a connected graph G, let A(G) be the adjacency matrix of G and D(G) be the diagonal matrix of the degrees of the vertices in G. The A_α-matrix of G is defined as A_α(G) = αD(G) + (1-α) A(G) for any α∈ [0,1]. The largest eigenvalue of A_α(G) is called the A_α-spectral radius of G. In this article, we characterize the graphs with maximum A_α-spectral radius among the class of unicyclic and bicyclic graphs of order n with fixed girth g. Also, we identify the unique graphs with maximum A_α-spectral radius among the class of unicyclic and bicyclic graphs of order n with k pendant vertices.

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