Extremal Matching Energy of Complements of Trees
Tingzeng Wu; Weigen Yan; Heping Zhang
Discussiones Mathematicae Graph Theory (2016)
- Volume: 36, Issue: 3, page 505-521
- ISSN: 2083-5892
Access Full Article
topAbstract
topHow to cite
topTingzeng Wu, Weigen Yan, and Heping Zhang. "Extremal Matching Energy of Complements of Trees." Discussiones Mathematicae Graph Theory 36.3 (2016): 505-521. <http://eudml.org/doc/285395>.
@article{TingzengWu2016,
abstract = {Gutman and Wagner proposed the concept of the matching energy which is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. And they pointed out that the chemical applications of matching energy go back to the 1970s. Let T be a tree with n vertices. In this paper, we characterize the trees whose complements have the maximal, second-maximal and minimal matching energy. Furthermore, we determine the trees with edge-independence number p whose complements have the minimum matching energy for p = 1, 2, . . . , [n/2]. When we restrict our consideration to all trees with a perfect matching, we determine the trees whose complements have the second-maximal matching energy.},
author = {Tingzeng Wu, Weigen Yan, Heping Zhang},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {matching polynomial; matching energy; Hosoya index; energy},
language = {eng},
number = {3},
pages = {505-521},
title = {Extremal Matching Energy of Complements of Trees},
url = {http://eudml.org/doc/285395},
volume = {36},
year = {2016},
}
TY - JOUR
AU - Tingzeng Wu
AU - Weigen Yan
AU - Heping Zhang
TI - Extremal Matching Energy of Complements of Trees
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 3
SP - 505
EP - 521
AB - Gutman and Wagner proposed the concept of the matching energy which is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. And they pointed out that the chemical applications of matching energy go back to the 1970s. Let T be a tree with n vertices. In this paper, we characterize the trees whose complements have the maximal, second-maximal and minimal matching energy. Furthermore, we determine the trees with edge-independence number p whose complements have the minimum matching energy for p = 1, 2, . . . , [n/2]. When we restrict our consideration to all trees with a perfect matching, we determine the trees whose complements have the second-maximal matching energy.
LA - eng
KW - matching polynomial; matching energy; Hosoya index; energy
UR - http://eudml.org/doc/285395
ER -
References
top- [1] J. Aihara, A new definition of Dewar-type resonance energies, J. Amer. Chem. Soc. 98 (1976) 2750-2758. doi:10.1021/ja00426a013[Crossref]
- [2] L. Chen and Y. Shi, The maximal matching energy of tricyclic graphs, MATCH Commun. Math. Comput. Chem. 73 (2015) 105-119.
- [3] L. Chen, J. Liu and Y. Shi, Matching energy of unicyclic and bicyclic graphs with a given diameter , Complexity 21 (2015) 224-238. doi:10.1002/cplx.21599[Crossref][WoS]
- [4] D. Cvetković, M. Doob, I. Gutman and A. Torgašev, Recent Results in the Theory of Graph Spectra (North-Holland, Amsterdam, 1988). Zbl0634.05054
- [5] M.J.S. Dewar, The Molecular Orbital Theory of Organic Chemistry (McGraw-Hill, New York, 1969).
- [6] E.J. Farrell, An introduction to matching polynomials, J. Combin. Theory Ser. B 27 (1979) 75-86. doi:10.1016/0095-8956(79)90070-4[Crossref]
- [7] C.D. Godsil, Algebraic Combinatorics (Chapman and Hall, New York, 1993).
- [8] C.D. Godsil and I. Gutman, On the theory of the matching polynomial , J. Graph Theory 5 (1981) 137-144. doi:10.1002/jgt.3190050203[Crossref]
- [9] I. Gutman, The matching polynomial , MATCH Commun. Math. Comput. Chem. 6 (1979) 75-91. Zbl0436.05053
- [10] I. Gutman and S. Wagner, The matching energy of a graph, Discrete Appl. Math. 160 (2012) 2177-2187. doi:10.1016/j.dam.2012.06.001[WoS][Crossref] Zbl1252.05120
- [11] I. Gutman, The energy of a graph: old and new results, in: Algebraic Combina- torics and Applications, A. Betten, A. Kohnert, R. Laue, A. Wassermann (Ed(s)), (Springer-Verlag, Berlin, 2001) 196-211. doi:10.1007/978-3-642-59448-9 13[Crossref] Zbl0974.05054
- [12] I. Gutman, X. Li and J. Zhang, Graph energy, in: Analysis of Complex Networks From Biology to Linguistics, M. Dehmer, F. Emmert-Streib (Ed(s)), (Wiley-VCH, Weinheim, 2009) 145-174. doi:10.1002/9783527627981.ch7[Crossref]
- [13] S. Ji, X. Li and Y. Shi, Extremal matching energy of bicyclic graphs, MATCH Commun. Math. Comput. Chem. 70 (2013) 697-706. Zbl1299.05220
- [14] H. Li, Y. Zhou and L. Su, Graphs with extremal matching energies and prescribed parameters, MATCH Commun. Math. Comput. Chem. 72 (2014) 239-248.
- [15] S. Li and W. Yan, The matching energy of graphs with given parameters, Discrete Appl. Math. 162 (2014) 415-420. doi:10.1016/j.dam.2013.09.014[WoS][Crossref] Zbl1300.05162
- [16] X. Li, Y. Shi and I. Gutman, Graph Energy (Springer, New York, 2012). doi:10.1007/978-1-4614-4220-2[Crossref]
- [17] L. Lovász, Combinatorial Problems and Exercises, Second Edition (Budapest, Akad´emiai Kiad´o, 1993). Zbl0785.05001
- [18] D.B. West, Introduction to Graph Theory, Second Edition (Pearson Education, Singapore, 2001).
- [19] T. Wu, On the maximal matching energy of graphs, J. East China Norm. Univ. 1 (2015) 136-141.
- [20] K. Xu, Z. Zheng and K.C. Das, Extremal t-apex trees with respect to matching energy, Complexity (2015), in press. doi:10.1002/cplx.21651[Crossref]
- [21] K. Xu, K.C. Das and Z. Zheng, The minimum matching energy of (n,m)-graphs with a given matching number , MATCH Commun. Math. Comput. Chem. 73 (2015) 93-104.
- [22] W. Yan, Y. Yeh and F. Zhang, Ordering the complements of trees by the number of maximum matchings, J. Quan. Chem. 1055 (2005) 131-141. doi:10.1002/qua.20688[Crossref]
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.