Clique polynomials of $2$-connected $K_{5}$-free chordal graphs

Abstract

In this paper, we give a generalization of the author's previous result about real rootedness of clique polynomials of connected $K_{4}$-free chordal graphs to the class of $2$-connected $K_{5}$-free chordal graphs. The main idea is based on the graph-theoretical interpretation of the second derivative of clique polynomials. Finally, we conclude the paper with several interesting open questions and conjectures.

Keywords

• Chordal Graphs
• Clique Polynomials
• Clique Roots
• Clique Value

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