Research Article
BibTex RIS Cite

Year 2021, Volume: 8 Issue: 1, 23 - 29, 15.01.2021

Hossein Teimoori Faal

https://doi.org/10.13069/jacodesmath.863113
Cited By: 1

Abstract

References

  • [1] J. A. Bondy, U. S. R. Murty, Graph theory, Springer GTM 244 (2008).
  • [2] P. Branden, Unimodality, log-concavity, real-rootedness and beyond, Handbook of Enumerative Combinatorics, CRC Perss (2018).
  • [3] L. Comet, Advanced combinatorics, 200. Reidel, Dordrecht-Boston (1974).
  • [4] H. Hajiabolhassan, M. L. Mehrabadi, On clique polynomials, Australasian Journal of Combinatorics 18 (1998) 313–316.
  • [5] P. Haxell, A. Kostochka, S. Thomasse, Packing and covering triangles in K4-free planar graphs, Discrete Applied Mathematics 28 (2012) 653–662.
  • [6] X. Li, I. Gutman, A unified approach to the first derivatives of graph polynomials, Discrete Applied Mathematics 587 (1995) 293–297.
  • [7] T. A. McKee, F. R. McMorris, Topics in intersection graph theory (Monographs on Discrete Mathematics and Applications), Society for Industrial and Applied Mathematics (1987).
  • [8] H. Teimoori, Clique roots of K4-free chordal graphs, Electronic Journal of Graph Theory and Applications 7(1) (2010) 105–111.
  • [9] A. A. Zykov, On some properties of linear complexes, Mat. Sbornik N.S. 24(66) (1949) 163–188.

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

Year 2021, Volume: 8 Issue: 1, 23 - 29, 15.01.2021

Hossein Teimoori Faal

https://doi.org/10.13069/jacodesmath.863113
Cited By: 1

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

References

  • [1] J. A. Bondy, U. S. R. Murty, Graph theory, Springer GTM 244 (2008).
  • [2] P. Branden, Unimodality, log-concavity, real-rootedness and beyond, Handbook of Enumerative Combinatorics, CRC Perss (2018).
  • [3] L. Comet, Advanced combinatorics, 200. Reidel, Dordrecht-Boston (1974).
  • [4] H. Hajiabolhassan, M. L. Mehrabadi, On clique polynomials, Australasian Journal of Combinatorics 18 (1998) 313–316.
  • [5] P. Haxell, A. Kostochka, S. Thomasse, Packing and covering triangles in K4-free planar graphs, Discrete Applied Mathematics 28 (2012) 653–662.
  • [6] X. Li, I. Gutman, A unified approach to the first derivatives of graph polynomials, Discrete Applied Mathematics 587 (1995) 293–297.
  • [7] T. A. McKee, F. R. McMorris, Topics in intersection graph theory (Monographs on Discrete Mathematics and Applications), Society for Industrial and Applied Mathematics (1987).
  • [8] H. Teimoori, Clique roots of K4-free chordal graphs, Electronic Journal of Graph Theory and Applications 7(1) (2010) 105–111.
  • [9] A. A. Zykov, On some properties of linear complexes, Mat. Sbornik N.S. 24(66) (1949) 163–188.
There are 9 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Hossein Teimoori Faal This is me 0000-0001-5861-6287

Publication Date January 15, 2021
Published in Issue Year 2021 Volume: 8 Issue: 1

Cite

APA Faal, H. T. (2021). Clique polynomials of $2$-connected $K_{5}$-free chordal graphs. Journal of Algebra Combinatorics Discrete Structures and Applications, 8(1), 23-29. https://doi.org/10.13069/jacodesmath.863113
AMA Faal HT. Clique polynomials of $2$-connected $K_{5}$-free chordal graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. January 2021;8(1):23-29. doi:10.13069/jacodesmath.863113
Chicago Faal, Hossein Teimoori. “Clique Polynomials of $2$-Connected $K_{5}$-Free Chordal Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications 8, no. 1 (January 2021): 23-29. https://doi.org/10.13069/jacodesmath.863113.
EndNote Faal HT (January 1, 2021) Clique polynomials of $2$-connected $K_{5}$-free chordal graphs. Journal of Algebra Combinatorics Discrete Structures and Applications 8 1 23–29.
IEEE H. T. Faal, “Clique polynomials of $2$-connected $K_{5}$-free chordal graphs”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 8, no. 1, pp. 23–29, 2021, doi: 10.13069/jacodesmath.863113.
ISNAD Faal, Hossein Teimoori. “Clique Polynomials of $2$-Connected $K_{5}$-Free Chordal Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications 8/1 (January2021), 23-29. https://doi.org/10.13069/jacodesmath.863113.
JAMA Faal HT. Clique polynomials of $2$-connected $K_{5}$-free chordal graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021;8:23–29.
MLA Faal, Hossein Teimoori. “Clique Polynomials of $2$-Connected $K_{5}$-Free Chordal Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 8, no. 1, 2021, pp. 23-29, doi:10.13069/jacodesmath.863113.
Vancouver Faal HT. Clique polynomials of $2$-connected $K_{5}$-free chordal graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021;8(1):23-9.

Cited By

Face-Counting Identities and Derivatives of Face Polynomials
Turkish Journal of Mathematics and Computer Science
https://doi.org/10.47000/tjmcs.1120399