Year: 2025
Type: article
Abstract: Let G be a graph with n vertices.For i = 1, 2, . . ., n, let di be the degree of vertex vi in G.The atom-bond sum-connectivity (ABS) matrix of G is an n × n matrix whose (i, j)-entry is equal to (di + dj -2)/(di + dj) if the vertices vi and vj are adjacent, and 0 otherwise.The ABS spectral radius of G, denoted by ρ1(G), is the largest eigenvalue of the ABS matrix of G. Let Cn be the cycle graph with n vertices.Let U 1 n be the unicyclic graph with n vertices and maximum degree n -1.For a unicyclic graph G with n ≥ 17 vertices, we prove that ρ1(Cn) ≤ ρ1(G) ≤ ρ1(U 1 n ), where the left equality holds if and only if G ∼ = Cn and the right equality holds if and only if G ∼ = U 1 n .
Source: Discrete Mathematics Letters
Authors: Zhen Lin, Yingke Liu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Qinghai Normal University
OpenAlex ID: W4410131273