On the spectral radius of graphs without a star forest
Ming-Zhu Chen, A-Ming Liu, Xiao-Dong Zhang
TL;DR
This paper establishes sharp upper bounds on the spectral radius of bipartite graphs avoiding a star forest, characterizes extremal graphs, and determines the minimum least eigenvalue for such graphs.
Contribution
It introduces new bounds and characterizations for the spectral properties of graphs with forbidden star forests, advancing spectral graph theory.
Findings
Sharp upper bounds for spectral radius of bipartite graphs without star forests
Characterization of extremal graphs achieving these bounds
Determination of minimum least eigenvalue for such graphs
Abstract
In this paper, we present two sharp upper bounds for the spectral radius of (bipartite) graphs with forbidden a star forest and characterize all extremal graphs. Moreover, the minimum least eigenvalue of the adjacency matrix of graph with forbidden a star forest and all extremal graphs for graphs are obtained.
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Taxonomy
TopicsGraph theory and applications · Graph Labeling and Dimension Problems · Matrix Theory and Algorithms