Kirchhoff index, multiplicative degree‐Kirchhoff index and spanning trees of the linear crossed hexagonal chains
Let Hn be a linear crossed hexagonal chain with n crossed hexagonals. In this article, we find that the Laplacian (resp. normalized Laplacian) spectrum of Hn consists of the eigenvalues of a symmetric tridiagonal matrix of order 2n + 1 and a diagonal matrix of order 2n + 1. Based on the properties o...
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| Veröffentlicht in: | International journal of quantum chemistry 2018-12, Vol.118 (24), p.n/a |
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| creator | Pan, Yingui Li, Jianping |
| description | Let Hn be a linear crossed hexagonal chain with n crossed hexagonals. In this article, we find that the Laplacian (resp. normalized Laplacian) spectrum of Hn consists of the eigenvalues of a symmetric tridiagonal matrix of order 2n + 1 and a diagonal matrix of order 2n + 1. Based on the properties of these matrices, significant closed formulas for the Kirchhoff index, multiplicative degree‐Kirchhoff index and the number of spanning trees of Hn are derived. Finally, we show that the Kirchhoff (resp. multiplicative degree‐Kirchhoff) index of Hn is approximately one quarter of its Wiener (resp. Gutman) index.
Based on the decomposition theorem of the Laplacian (resp. normalized Laplacian) polynomial, significant closed formulas for the Kirchhoff index, multiplicative degree‐Kirchhoff index, and the number of spanning trees are derived. In addition, the Kirchhoff (resp. multiplicative degree‐Kirchhoff) index is found to be approximately one quarter of its Wiener (resp. Gutman) index. |
| doi_str_mv | 10.1002/qua.25787 |
| format | Article |
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Based on the decomposition theorem of the Laplacian (resp. normalized Laplacian) polynomial, significant closed formulas for the Kirchhoff index, multiplicative degree‐Kirchhoff index, and the number of spanning trees are derived. In addition, the Kirchhoff (resp. multiplicative degree‐Kirchhoff) index is found to be approximately one quarter of its Wiener (resp. Gutman) index.</description><identifier>ISSN: 0020-7608</identifier><identifier>EISSN: 1097-461X</identifier><identifier>DOI: 10.1002/qua.25787</identifier><language>eng</language><publisher>Hoboken, USA: John Wiley & Sons, Inc</publisher><subject>Chains ; Chemistry ; Eigenvalues ; Graph theory ; Gutman index ; Kirchhoff index ; Mathematical analysis ; Matrix methods ; multiplicative degree‐Kirchhoff index ; Physical chemistry ; Quantum physics ; spanning tree ; Wiener index</subject><ispartof>International journal of quantum chemistry, 2018-12, Vol.118 (24), p.n/a</ispartof><rights>2018 Wiley Periodicals, Inc.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3327-c75ef270253b82b48f29312b3b1687991a35a5a8b406548ca0883b4cd02c25be3</citedby><cites>FETCH-LOGICAL-c3327-c75ef270253b82b48f29312b3b1687991a35a5a8b406548ca0883b4cd02c25be3</cites><orcidid>0000-0001-7569-6223</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fqua.25787$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fqua.25787$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1416,27922,27923,45572,45573</link.rule.ids></links><search><creatorcontrib>Pan, Yingui</creatorcontrib><creatorcontrib>Li, Jianping</creatorcontrib><title>Kirchhoff index, multiplicative degree‐Kirchhoff index and spanning trees of the linear crossed hexagonal chains</title><title>International journal of quantum chemistry</title><description>Let Hn be a linear crossed hexagonal chain with n crossed hexagonals. In this article, we find that the Laplacian (resp. normalized Laplacian) spectrum of Hn consists of the eigenvalues of a symmetric tridiagonal matrix of order 2n + 1 and a diagonal matrix of order 2n + 1. Based on the properties of these matrices, significant closed formulas for the Kirchhoff index, multiplicative degree‐Kirchhoff index and the number of spanning trees of Hn are derived. Finally, we show that the Kirchhoff (resp. multiplicative degree‐Kirchhoff) index of Hn is approximately one quarter of its Wiener (resp. Gutman) index.
Based on the decomposition theorem of the Laplacian (resp. normalized Laplacian) polynomial, significant closed formulas for the Kirchhoff index, multiplicative degree‐Kirchhoff index, and the number of spanning trees are derived. In addition, the Kirchhoff (resp. multiplicative degree‐Kirchhoff) index is found to be approximately one quarter of its Wiener (resp. Gutman) index.</description><subject>Chains</subject><subject>Chemistry</subject><subject>Eigenvalues</subject><subject>Graph theory</subject><subject>Gutman index</subject><subject>Kirchhoff index</subject><subject>Mathematical analysis</subject><subject>Matrix methods</subject><subject>multiplicative degree‐Kirchhoff index</subject><subject>Physical chemistry</subject><subject>Quantum physics</subject><subject>spanning tree</subject><subject>Wiener index</subject><issn>0020-7608</issn><issn>1097-461X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp10N1KwzAUB_AgCs7phW8Q8EqwWz7aJL0c4hcORHDgXUjTdM3o0i5pdbvzEXxGn8S6eiV4dS7O7xz-_AE4x2iCESLTTacmJOGCH4ARRimPYoZfD8Go36GIMySOwUkIK4QQo4yPgH-0XpdlXRTQutxsr-C6q1rbVFar1r4ZmJulN-br4_MPhMrlMDTKOeuWsO1NgHUB29LAyjqjPNS-DsHksDRbtaydqqAulXXhFBwVqgrm7HeOweL25uX6Ppo_3T1cz-aRppTwSPPEFIQjktBMkCwWBUkpJhnNMBM8TbGiiUqUyGLEklhohYSgWaxzRDRJMkPH4GL42_h605nQylXd-T5HkARTnMaMsLRXl4Pax_WmkI23a-V3EiP5U6nsK5X7Sns7Hey7rczufyifF7Ph4huSL3ni</recordid><startdate>20181215</startdate><enddate>20181215</enddate><creator>Pan, Yingui</creator><creator>Li, Jianping</creator><general>John Wiley & Sons, Inc</general><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-7569-6223</orcidid></search><sort><creationdate>20181215</creationdate><title>Kirchhoff index, multiplicative degree‐Kirchhoff index and spanning trees of the linear crossed hexagonal chains</title><author>Pan, Yingui ; Li, Jianping</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3327-c75ef270253b82b48f29312b3b1687991a35a5a8b406548ca0883b4cd02c25be3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Chains</topic><topic>Chemistry</topic><topic>Eigenvalues</topic><topic>Graph theory</topic><topic>Gutman index</topic><topic>Kirchhoff index</topic><topic>Mathematical analysis</topic><topic>Matrix methods</topic><topic>multiplicative degree‐Kirchhoff index</topic><topic>Physical chemistry</topic><topic>Quantum physics</topic><topic>spanning tree</topic><topic>Wiener index</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pan, Yingui</creatorcontrib><creatorcontrib>Li, Jianping</creatorcontrib><collection>CrossRef</collection><jtitle>International journal of quantum chemistry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pan, Yingui</au><au>Li, Jianping</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Kirchhoff index, multiplicative degree‐Kirchhoff index and spanning trees of the linear crossed hexagonal chains</atitle><jtitle>International journal of quantum chemistry</jtitle><date>2018-12-15</date><risdate>2018</risdate><volume>118</volume><issue>24</issue><epage>n/a</epage><issn>0020-7608</issn><eissn>1097-461X</eissn><abstract>Let Hn be a linear crossed hexagonal chain with n crossed hexagonals. In this article, we find that the Laplacian (resp. normalized Laplacian) spectrum of Hn consists of the eigenvalues of a symmetric tridiagonal matrix of order 2n + 1 and a diagonal matrix of order 2n + 1. Based on the properties of these matrices, significant closed formulas for the Kirchhoff index, multiplicative degree‐Kirchhoff index and the number of spanning trees of Hn are derived. Finally, we show that the Kirchhoff (resp. multiplicative degree‐Kirchhoff) index of Hn is approximately one quarter of its Wiener (resp. Gutman) index.
Based on the decomposition theorem of the Laplacian (resp. normalized Laplacian) polynomial, significant closed formulas for the Kirchhoff index, multiplicative degree‐Kirchhoff index, and the number of spanning trees are derived. In addition, the Kirchhoff (resp. multiplicative degree‐Kirchhoff) index is found to be approximately one quarter of its Wiener (resp. Gutman) index.</abstract><cop>Hoboken, USA</cop><pub>John Wiley & Sons, Inc</pub><doi>10.1002/qua.25787</doi><tpages>15</tpages><orcidid>https://orcid.org/0000-0001-7569-6223</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Chains Chemistry Eigenvalues Graph theory Gutman index Kirchhoff index Mathematical analysis Matrix methods multiplicative degree‐Kirchhoff index Physical chemistry Quantum physics spanning tree Wiener index |
| title | Kirchhoff index, multiplicative degree‐Kirchhoff index and spanning trees of the linear crossed hexagonal chains |
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