On the general ‎ABC-spectral radius and ABC-energy of a graph

Hayati, Kianoosh; Shaveisi, Farzad

doi:10.22061/jdma.2026.12740.1182

On the general ‎ABC-spectral radius and ABC-energy of a graph

Document Type : Full Length Article

Authors

Kianoosh Hayati ¹
Farzad Shaveisi ²

¹ Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran

² Department of Mathematics, Faculty of Science Kermanshah, 6714967346, Iran

10.22061/jdma.2026.12740.1182

Abstract

Let G be a simple graph with vertex set {v₁, v₂,…, v_n} where d_i denotes the degree of v_i. For every real number α, the generalized ABC-matrix of G, denoted by Ω^α=[ω^α_ij] is an n×n matrix such that ω^α_ij=((d_i + d_j - 2)/d_id_j)^α if v_iv_j is an edge and ω^α_ij=0, otherwise. In this paper, some bounds for the spectral radius of Ω_α are found. Among other results, some bounds for the generalized ABC-energy are determined in terms of generalized ABC-index and general Randić index.

Graphical Abstract

Keywords

Main Subjects

Chemical Graph Theory

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