Extremal Graphs with Respect to Matching Energy for Random Six-membered Ring Spiro Chains
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摘要
Gutman and Wagner(in the matching energy of a graph, Disc. Appl. Math., 2012) defined the matching energy of a graph and pointed out that its chemical applications go back to the 1970 s. Now the research on matching energy mainly focuses on graphs with pendent vertices and only a few papers reported the progress on matching energy of graphs without pendent vertices. For a random six-membered ring spiro chain, the number of k-matchings and the matching energy are random variables. In this paper, we determine the extremal graphs with respect to the matching energy for random six-membered ring spiro chains which have no pendent vertices.
Gutman and Wagner(in the matching energy of a graph, Disc. Appl. Math., 2012) defined the matching energy of a graph and pointed out that its chemical applications go back to the 1970 s. Now the research on matching energy mainly focuses on graphs with pendent vertices and only a few papers reported the progress on matching energy of graphs without pendent vertices. For a random six-membered ring spiro chain, the number of k-matchings and the matching energy are random variables. In this paper, we determine the extremal graphs with respect to the matching energy for random six-membered ring spiro chains which have no pendent vertices.
Gutman and Wagner(in the matching energy of a graph, Disc. Appl. Math., 2012) defined the matching energy of a graph and pointed out that its chemical applications go back to the 1970 s. Now the research on matching energy mainly focuses on graphs with pendent vertices and only a few papers reported the progress on matching energy of graphs without pendent vertices. For a random six-membered ring spiro chain, the number of k-matchings and the matching energy are random variables. In this paper, we determine the extremal graphs with respect to the matching energy for random six-membered ring spiro chains which have no pendent vertices.
引文
[13]Chen,L.,Liu,J.,Shi,Y.Matching energy of unicyclic and bicyclic graphs with a given diameter.Complexity,21(2):224-238(2015)
[14]Chen L,Liu,J.,Shi,Y.Bounds on the matching energy of unicyclic odd-cycle graphs.MATCH Commun.Math.Comput.Chem.,75(2):315-330(2016)
[6]Chen,L.,Shi,Y.Maximal matching energy of tricyclic graphs.MATCH Commun.Math.Comput.Chem.,73:105-119(2015)
[2]Chen,X.,Zhao,B.,Zhao,P.Six-membered ring spiro chains with extremal Merrifield-Simmons index and Hosoya index.MATCH Commun.Math.Comput.Chem.,62:657-665(2009)
[8]Farrell,E.J.An introduction to matching polynomials.J.Comb.Theory B,27:75-86(1979)
[3]Gutman,I.Acyclic systems with extremal H¨uckelπ-electron energy.Theor.Chim.Acta,45:79-87(1977)
[9]Gutman,I.The matching polynomial.MATCH Commun.Math.Comput.Chem.,6:75-91(1979)
[1]Gutman,I.,Wagner,S.The matching energy of a graph.Discr.Appl.Math.,160:2177-2187(2012)
[7]Huang,G.,Kuang,M.,Deng,H.Extremal graph with respect to matching energy for a random polyphenyl chain.MATCH Commun.Math.Comput.Chem.,73:121-131(2015)
[5]Ji,S.,Li,X.,Shi,Y.Extremal matching energy of bicyclic graphs.MATCH Commun.Math.Comput.Chem.,70:697-706(2013)
[12]Li,X.,Shi,Y.,Gutman,I.Graph Energy,Springer,New York,2012
[11]Li,H.,Zhou,Y.,Su,L.Graphs with extremal matching energies and prescribed parameters.MATCHCommun.Math.Comput.Chem.,72:239-248(2014)
[10]Mar′?n,C.A.,Monsalve,J.,Rada,J.Maximum and minimum energy trees with two and three branched vertices.MATCH Commun.Math.Comput.Chem.,74:285-306(2015)
[4]Wang,W.,So,W.On minimum matching energy of graphs.MATCH Commun.Math.Comput.Chem.,74:399-410(2015)
[14]Chen L,Liu,J.,Shi,Y.Bounds on the matching energy of unicyclic odd-cycle graphs.MATCH Commun.Math.Comput.Chem.,75(2):315-330(2016)
[6]Chen,L.,Shi,Y.Maximal matching energy of tricyclic graphs.MATCH Commun.Math.Comput.Chem.,73:105-119(2015)
[2]Chen,X.,Zhao,B.,Zhao,P.Six-membered ring spiro chains with extremal Merrifield-Simmons index and Hosoya index.MATCH Commun.Math.Comput.Chem.,62:657-665(2009)
[8]Farrell,E.J.An introduction to matching polynomials.J.Comb.Theory B,27:75-86(1979)
[3]Gutman,I.Acyclic systems with extremal H¨uckelπ-electron energy.Theor.Chim.Acta,45:79-87(1977)
[9]Gutman,I.The matching polynomial.MATCH Commun.Math.Comput.Chem.,6:75-91(1979)
[1]Gutman,I.,Wagner,S.The matching energy of a graph.Discr.Appl.Math.,160:2177-2187(2012)
[7]Huang,G.,Kuang,M.,Deng,H.Extremal graph with respect to matching energy for a random polyphenyl chain.MATCH Commun.Math.Comput.Chem.,73:121-131(2015)
[5]Ji,S.,Li,X.,Shi,Y.Extremal matching energy of bicyclic graphs.MATCH Commun.Math.Comput.Chem.,70:697-706(2013)
[12]Li,X.,Shi,Y.,Gutman,I.Graph Energy,Springer,New York,2012
[11]Li,H.,Zhou,Y.,Su,L.Graphs with extremal matching energies and prescribed parameters.MATCHCommun.Math.Comput.Chem.,72:239-248(2014)
[10]Mar′?n,C.A.,Monsalve,J.,Rada,J.Maximum and minimum energy trees with two and three branched vertices.MATCH Commun.Math.Comput.Chem.,74:285-306(2015)
[4]Wang,W.,So,W.On minimum matching energy of graphs.MATCH Commun.Math.Comput.Chem.,74:399-410(2015)