The Sum and Product of Independence Numbers of Graphs and their Line Graphs
Susanth C, Sunny Joseph Kalayathankal
TL;DR
This paper investigates bounds on the sum and product of independence numbers of graphs and their line graphs, extending Nordhaus-Gaddum type inequalities to these parameters.
Contribution
It introduces new bounds on the independence numbers of graphs and their line graphs, expanding the scope of Nordhaus-Gaddum inequalities.
Findings
Derived bounds for the sum of independence numbers
Established bounds for the product of independence numbers
Extended Nordhaus-Gaddum inequalities to independence numbers
Abstract
The bounds on the sum and product of chromatic numbers of a graph and its complement are known as Nordhaus-Gaddum inequalities. In this paper, we study the bounds on the sum and product of the independence numbers of graphs and their line graphs.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Graph theory and applications · Advanced Graph Theory Research