Work

On the spectral radius of bipartite graphs with given order and 4-independence number

Year: 2025

Type: article

Abstract: For a positive integer k, let Pk be a path of order k. For a graph G, a subset S ⊆ V (G) is called a k-independent set if the induced subgraph G[S] does not contain Pk as its subgraph. The k-independence number of G, denoted by αk(G), is the maximum cardinality of a k-independent set in G. Let Bn,αk be the set of bipartite graphs of order n with k-independence number αk. What are the corresponding extremal graphs in Bn,αk with the maximum spectral radius? Lou and Guo [Discrete Math. 345 (2022) 112778] solved the problem for k = 2, and then Huang et al. [Discrete Appl. Math. 342 (2024) 368–380] provided the answer for k = 3. We are interested in the analogous problem for k = 4. In the paper, we determine the unique graph attaining the maximum spectral radius among all bipartite graphs in Bn,α4.

Source: RAIRO - Operations Research

DOI: 10.1051/ro/2025073

Authors: Wenxiu Ding, Dan Li

Institution: Xinjiang University

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Natural Science Foundation of Xinjiang Province, National Natural Science Foundation of China

Awards: G1103760527, G6294865353