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Matchings in Tetrameric 1, 3-Adamantane

Year 2018, Volume: 6 Issue: 1, 149 - 152, 15.04.2018

Abstract

Suppose $G$ is a graph, $A(G)$ its adjacency matrix, and $\varphi(G,\lambda)=\sum_{i=0}^{n} a_i \lambda^{n-i}$ is the characteristic polynomial of $G$. The polynomial $M(G,x)=\sum_{k \geq 0}(-1)^{k} m(G,k) x^{n-2k}$, is called the matching polynomial of $G$, where $m(G,k)$ is the number of $k-$matchings in $G$. In this paper, we consider tetrameric 1, 3-adamantane, $TA(N)$, and determine some coefficients of characteristic polynomial and matching polynomial of $TA(N)$.

References

  • [1] Ashrafi A.R. and Fath-Tabar G.H. , Bounds on the Estrada index of ISR(4;6)􀀀fullerene, Appl. Math. Lett., 24, (2011) 337-339.
  • [2] Behmaram A., On the number of 4􀀀matchings in graphs, MATCH Commun. Math. Comput. Chem. 62, (2009) 381-388.
  • [3] Biggs N., Algebraic Graph Theory, Cambridge Univ, Press, Cambridge (1974).
  • [4] Cvetkovi´c D., Doob M. and Sachs H., Spectra of Graphs-Theory and Applications, Academic Press, New York (1980).
  • [5] Fath-Tabar G.H., Dosli´c T. and Ashrafi A.R., On the Szeged and the Laplacian Szeged spectrum of a graph, Linear Algebra Appl., 433, (2010) 662- 671.
  • [6] Fath-Tabar G.H. and Ashrafi A.R., New upper bounds for Estrada index of bipartite graph, Linear Algebra. Appl., 435, (2011) 2607-2611.
  • [7] Godsil C.D. and Gutman I., Some remarks on the matching polynomial and its zeros, Croat. Chem. Acta 54, (1981) 53-59.
  • [8] C.D. Godsil and I. Gutman, On the theory of the matching polynomial, J. Graph Theory, 5, 137-144 (1981).
  • [9] Gutman I., The matching polynomial, MATCH Commun. Math.Comput. Chem. 6, (1979) 75-91.
  • [10] Gutman I., Milun M. Trinajsti´c and N., Non-Parametric Resonance Energies of Arbitrary Conjugated Systems, J. Am. Chem. Soc. 99, (1977) 1692-1704.
  • [11] Riordan J., An Introduction to Combinatorial Analysis, Wiley, New York (1958).
  • [12] Taghvaee F. and Ashrafi A.R., Comparing fullerenes by spectral moments, J. Nanosci. Nanotechnol., 16, (2016) 1-4.
  • [13] Taghvaee F. and Fath-Tabar G.H., Signless Laplacian spectral moments of graphs and ordering some graphs with respect to them, Alg. Struc. Appl., 1, (2014) 133-141.
  • [14] Taghvaee F. and Fath-Tabar G.H., Relationship between coefficients of characteristic polynomial and matching polynomial of regular graphs and its applications, Iranian J. Math. Chem., 8 (2017), 7-23.
  • [15] Vesalian R. and Asgari F., Number of 5􀀀matchings in graphs, MATCH Commun. Math. Comput. Chem., 69 (2013), 33-46.
  • [16] Wu Y., and Liu H., Lexicographical ordering by spectral moments of trees with a prescribed diameter, Linear Algebra Appl., 433 (2010), 1707-1713.
Year 2018, Volume: 6 Issue: 1, 149 - 152, 15.04.2018

Abstract

References

  • [1] Ashrafi A.R. and Fath-Tabar G.H. , Bounds on the Estrada index of ISR(4;6)􀀀fullerene, Appl. Math. Lett., 24, (2011) 337-339.
  • [2] Behmaram A., On the number of 4􀀀matchings in graphs, MATCH Commun. Math. Comput. Chem. 62, (2009) 381-388.
  • [3] Biggs N., Algebraic Graph Theory, Cambridge Univ, Press, Cambridge (1974).
  • [4] Cvetkovi´c D., Doob M. and Sachs H., Spectra of Graphs-Theory and Applications, Academic Press, New York (1980).
  • [5] Fath-Tabar G.H., Dosli´c T. and Ashrafi A.R., On the Szeged and the Laplacian Szeged spectrum of a graph, Linear Algebra Appl., 433, (2010) 662- 671.
  • [6] Fath-Tabar G.H. and Ashrafi A.R., New upper bounds for Estrada index of bipartite graph, Linear Algebra. Appl., 435, (2011) 2607-2611.
  • [7] Godsil C.D. and Gutman I., Some remarks on the matching polynomial and its zeros, Croat. Chem. Acta 54, (1981) 53-59.
  • [8] C.D. Godsil and I. Gutman, On the theory of the matching polynomial, J. Graph Theory, 5, 137-144 (1981).
  • [9] Gutman I., The matching polynomial, MATCH Commun. Math.Comput. Chem. 6, (1979) 75-91.
  • [10] Gutman I., Milun M. Trinajsti´c and N., Non-Parametric Resonance Energies of Arbitrary Conjugated Systems, J. Am. Chem. Soc. 99, (1977) 1692-1704.
  • [11] Riordan J., An Introduction to Combinatorial Analysis, Wiley, New York (1958).
  • [12] Taghvaee F. and Ashrafi A.R., Comparing fullerenes by spectral moments, J. Nanosci. Nanotechnol., 16, (2016) 1-4.
  • [13] Taghvaee F. and Fath-Tabar G.H., Signless Laplacian spectral moments of graphs and ordering some graphs with respect to them, Alg. Struc. Appl., 1, (2014) 133-141.
  • [14] Taghvaee F. and Fath-Tabar G.H., Relationship between coefficients of characteristic polynomial and matching polynomial of regular graphs and its applications, Iranian J. Math. Chem., 8 (2017), 7-23.
  • [15] Vesalian R. and Asgari F., Number of 5􀀀matchings in graphs, MATCH Commun. Math. Comput. Chem., 69 (2013), 33-46.
  • [16] Wu Y., and Liu H., Lexicographical ordering by spectral moments of trees with a prescribed diameter, Linear Algebra Appl., 433 (2010), 1707-1713.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Fatemeh Taghvaee This is me

Gholam Hossein Fath-tabar

Publication Date April 15, 2018
Submission Date October 10, 2017
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Taghvaee, F., & Fath-tabar, G. H. (2018). Matchings in Tetrameric 1, 3-Adamantane. Konuralp Journal of Mathematics, 6(1), 149-152.
AMA Taghvaee F, Fath-tabar GH. Matchings in Tetrameric 1, 3-Adamantane. Konuralp J. Math. April 2018;6(1):149-152.
Chicago Taghvaee, Fatemeh, and Gholam Hossein Fath-tabar. “Matchings in Tetrameric 1, 3-Adamantane”. Konuralp Journal of Mathematics 6, no. 1 (April 2018): 149-52.
EndNote Taghvaee F, Fath-tabar GH (April 1, 2018) Matchings in Tetrameric 1, 3-Adamantane. Konuralp Journal of Mathematics 6 1 149–152.
IEEE F. Taghvaee and G. H. Fath-tabar, “Matchings in Tetrameric 1, 3-Adamantane”, Konuralp J. Math., vol. 6, no. 1, pp. 149–152, 2018.
ISNAD Taghvaee, Fatemeh - Fath-tabar, Gholam Hossein. “Matchings in Tetrameric 1, 3-Adamantane”. Konuralp Journal of Mathematics 6/1 (April 2018), 149-152.
JAMA Taghvaee F, Fath-tabar GH. Matchings in Tetrameric 1, 3-Adamantane. Konuralp J. Math. 2018;6:149–152.
MLA Taghvaee, Fatemeh and Gholam Hossein Fath-tabar. “Matchings in Tetrameric 1, 3-Adamantane”. Konuralp Journal of Mathematics, vol. 6, no. 1, 2018, pp. 149-52.
Vancouver Taghvaee F, Fath-tabar GH. Matchings in Tetrameric 1, 3-Adamantane. Konuralp J. Math. 2018;6(1):149-52.
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