Lower bounds for algebraic connectivity of graphs in terms of matching number or edge covering number
Jing Xu, Yi-Zheng Fan, Ying-Ying Tan
TL;DR
This paper establishes lower bounds for the algebraic connectivity of graphs based on their matching number or edge covering number, and characterizes the unique graphs that attain these bounds.
Contribution
It provides new lower bounds for algebraic connectivity related to matching and edge covering numbers, and identifies the unique extremal graphs.
Findings
Derived lower bounds for algebraic connectivity based on matching and edge covering numbers.
Characterized the unique graphs with minimum algebraic connectivity given these parameters.
Identified the extremal graphs that achieve the bounds.
Abstract
In this paper we characterize the unique graph whose algebraic connectivity is minimum among all connected graphs with given order and fixed matching number or edge covering number, and present two lower bounds for the algebraic connectivity in terms of the matching number or edge covering number.
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Taxonomy
TopicsGraph theory and applications · Graph Labeling and Dimension Problems · Interconnection Networks and Systems