Extremal Graphs with Respect to Matching Energy for Random Six-membered Ring Spiro Chains
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 1970s. Now the research on matching energy mainly focuses on graphs with pendent vertices and only a few papers reported...
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| Published in | Acta Mathematicae Applicatae Sinica Vol. 35; no. 2; pp. 319 - 326 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.04.2019
Springer Nature B.V |
| Edition | English series |
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| ISSN | 0168-9673 1618-3932 |
| DOI | 10.1007/s10255-019-0820-z |
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| Abstract | 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 1970s. 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. |
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| AbstractList | 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 1970s. 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 1970s. 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. |
| Author | Liu, Yan Chen, Hua-mei |
| Author_xml | – sequence: 1 givenname: Hua-mei surname: Chen fullname: Chen, Hua-mei organization: School of Mathematical Sciences, South China Normal University – sequence: 2 givenname: Yan surname: Liu fullname: Liu, Yan email: liuyan@scnu.edu.cn organization: School of Mathematical Sciences, South China Normal University |
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| Keywords | six-membered ring spiro chains random matching energy |
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| References | Farrell (CR5) 1979; 27 Li, Shi, Gutman (CR11) 2012 Gutman (CR7) 1979; 6 Chen, Zhao, Zhao (CR4) 2009; 62 Ji, Li, Shi (CR10) 2013; 70 Gutman, Wagner (CR8) 2012; 160 Huang, Kuang, Deng (CR9) 2015; 73 Chen, Liu, Shi (CR2) 2016; 75 Wang, So (CR14) 2015; 74 Gutman (CR6) 1977; 45 Marin, Monsalve, Rada (CR13) 2015; 74 Chen, Shi (CR3) 2015; 73 Chen, Liu, Shi (CR1) 2015; 21 Li, Zhou, Su (CR12) 2014; 72 L Chen (820_CR2) 2016; 75 I Gutman (820_CR6) 1977; 45 H Li (820_CR12) 2014; 72 W Wang (820_CR14) 2015; 74 G Huang (820_CR9) 2015; 73 X Chen (820_CR4) 2009; 62 X Li (820_CR11) 2012 L Chen (820_CR3) 2015; 73 L Chen (820_CR1) 2015; 21 I Gutman (820_CR7) 1979; 6 S Ji (820_CR10) 2013; 70 EJ Farrell (820_CR5) 1979; 27 I Gutman (820_CR8) 2012; 160 CA Marin (820_CR13) 2015; 74 |
| References_xml | – volume: 74 start-page: 399 year: 2015 end-page: 410 ident: CR14 article-title: On minimum matching energy of graphs publication-title: MATCH Commun. Math. Comput. Chem. – volume: 21 start-page: 224 issue: 2 year: 2015 end-page: 238 ident: CR1 article-title: Matching energy of unicyclic and bicyclic graphs with a given diameter publication-title: Complexity doi: 10.1002/cplx.21599 – volume: 62 start-page: 657 year: 2009 end-page: 665 ident: CR4 article-title: Six-membered ring spiro chains with extremal Merrifield-Simmons index and Hosoya index publication-title: MATCH Commun. Math. Comput. Chem. – volume: 6 start-page: 75 year: 1979 end-page: 91 ident: CR7 article-title: The matching polynomial publication-title: MATCH Commun. Math. Comput. Chem. – volume: 72 start-page: 239 year: 2014 end-page: 248 ident: CR12 article-title: Graphs with extremal matching energies and prescribed parameters publication-title: MATCH Commun. Math. Comput. Chem. – volume: 160 start-page: 2177 year: 2012 end-page: 2187 ident: CR8 article-title: The matching energy of a graph publication-title: Discr. Appl. Math. doi: 10.1016/j.dam.2012.06.001 – volume: 27 start-page: 75 year: 1979 end-page: 86 ident: CR5 article-title: An introduction to matching polynomials publication-title: J. Comb. Theory B doi: 10.1016/0095-8956(79)90070-4 – year: 2012 ident: CR11 publication-title: Graph Energy doi: 10.1007/978-1-4614-4220-2 – volume: 73 start-page: 105 year: 2015 end-page: 119 ident: CR3 article-title: Maximal matching energy of tricyclic graphs publication-title: MATCH Commun. Math. Comput. Chem. – volume: 45 start-page: 79 year: 1977 end-page: 87 ident: CR6 article-title: Acyclic systems with extremal Hückel π-electron energy publication-title: Theor. Chim. Acta doi: 10.1007/BF00552542 – volume: 73 start-page: 121 year: 2015 end-page: 131 ident: CR9 article-title: Extremal graph with respect to matching energy for a random polyphenyl chain publication-title: MATCH Commun. Math. Comput. Chem. – volume: 70 start-page: 697 year: 2013 end-page: 706 ident: CR10 article-title: Extremal matching energy of bicyclic graphs publication-title: MATCH Commun. Math. Comput. Chem. – volume: 74 start-page: 285 year: 2015 end-page: 306 ident: CR13 article-title: Maximum and minimum energy trees with two and three branched vertices publication-title: MATCH Commun. Math. Comput. Chem. – volume: 75 start-page: 315 issue: 2 year: 2016 end-page: 330 ident: CR2 article-title: Bounds on the matching energy of unicyclic odd-cycle graphs publication-title: MATCH Commun. Math. Comput. Chem. – volume: 75 start-page: 315 issue: 2 year: 2016 ident: 820_CR2 publication-title: MATCH Commun. Math. Comput. Chem. – volume-title: Graph Energy year: 2012 ident: 820_CR11 doi: 10.1007/978-1-4614-4220-2 – volume: 74 start-page: 285 year: 2015 ident: 820_CR13 publication-title: MATCH Commun. Math. Comput. Chem. – volume: 70 start-page: 697 year: 2013 ident: 820_CR10 publication-title: MATCH Commun. Math. Comput. Chem. – volume: 27 start-page: 75 year: 1979 ident: 820_CR5 publication-title: J. Comb. Theory B doi: 10.1016/0095-8956(79)90070-4 – volume: 45 start-page: 79 year: 1977 ident: 820_CR6 publication-title: Theor. Chim. Acta doi: 10.1007/BF00552542 – volume: 6 start-page: 75 year: 1979 ident: 820_CR7 publication-title: MATCH Commun. Math. Comput. Chem. – volume: 21 start-page: 224 issue: 2 year: 2015 ident: 820_CR1 publication-title: Complexity doi: 10.1002/cplx.21599 – volume: 62 start-page: 657 year: 2009 ident: 820_CR4 publication-title: MATCH Commun. Math. Comput. Chem. – volume: 74 start-page: 399 year: 2015 ident: 820_CR14 publication-title: MATCH Commun. Math. Comput. Chem. – volume: 73 start-page: 105 year: 2015 ident: 820_CR3 publication-title: MATCH Commun. Math. Comput. Chem. – volume: 160 start-page: 2177 year: 2012 ident: 820_CR8 publication-title: Discr. Appl. Math. doi: 10.1016/j.dam.2012.06.001 – volume: 73 start-page: 121 year: 2015 ident: 820_CR9 publication-title: MATCH Commun. Math. Comput. Chem. – volume: 72 start-page: 239 year: 2014 ident: 820_CR12 publication-title: MATCH Commun. Math. Comput. Chem. |
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| SubjectTerms | Apexes Applications of Mathematics Chains Energy Graph matching Graphs Math Applications in Computer Science Mathematical and Computational Physics Mathematics Mathematics and Statistics Organic chemistry Random variables Theoretical |
| Title | Extremal Graphs with Respect to Matching Energy for Random Six-membered Ring Spiro Chains |
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