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Year 2021, , 23 - 29, 15.01.2021
https://doi.org/10.13069/jacodesmath.863113

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, , 23 - 29, 15.01.2021
https://doi.org/10.13069/jacodesmath.863113

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.

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 Articles
Authors

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

Publication Date January 15, 2021
Published in Issue Year 2021

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 (January 2021), 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.