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## Discussiones Mathematicae Graph Theory

2016 | 36 | 3 | 505-521
Tytuł artykułu

### Extremal Matching Energy of Complements of Trees

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
EN
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
505-521
Opis fizyczny
Daty
wydano
2016-08-01
otrzymano
2015-02-01
poprawiono
2015-08-09
zaakceptowano
2015-08-09
online
2016-07-06
Twórcy
autor
• School of Mathematics and Statistics Qinghai Nationalities University Xining, Qinghai 810007, P.R. China, mathtzwu@163.com
autor
autor
• School of Mathematics and Statistics, Lanzhou University Lanzhou, Gansu 730000, P.R. China, zhanghp@lzu.edu.cn
Bibliografia
• [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).
• [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.
• [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]
• [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]
• [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.
• [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]
• [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).
• [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]
Typ dokumentu
Bibliografia
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