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Construction of L-equienergetic graphs using some graph operations
For a graph G with n vertices and m edges, the eigenvalues of its adjacency matrix A(G) are known as eigenvalues of G. The sum of absolute values of eigenvalues of G is called the energy of G. The Laplacian matrix of G is defined as where D(G) is the diagonal matrix with entry is the degree of verte...
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| Published in: | AKCE international journal of graphs and combinatorics 2020-09, Vol.ahead-of-print (ahead-of-print), p.1-6 |
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| container_title | AKCE international journal of graphs and combinatorics |
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| creator | Vaidya, S. K. Popat, Kalpesh M. |
| description | For a graph G with n vertices and m edges, the eigenvalues of its adjacency matrix A(G) are known as eigenvalues of G. The sum of absolute values of eigenvalues of G is called the energy of G. The Laplacian matrix of G is defined as
where D(G) is the diagonal matrix with
entry is the degree of vertex v
i
. The collection of eigenvalues of L(G) with their multiplicities is called spectra of L(G). If
are the eigenvalues of L(G) then the Laplacian energy LE(G) of G is defined as
It is always interesting and challenging as well to investigate the graphs which are L-equienergetic but L-noncopectral as L-cospectral graphs are obviously L-equienergetic. We have devised a method to construct L-equienergetic graphs which are L-noncospectral. |
| doi_str_mv | 10.1016/j.akcej.2019.06.012 |
| format | article |
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where D(G) is the diagonal matrix with
entry is the degree of vertex v
i
. The collection of eigenvalues of L(G) with their multiplicities is called spectra of L(G). If
are the eigenvalues of L(G) then the Laplacian energy LE(G) of G is defined as
It is always interesting and challenging as well to investigate the graphs which are L-equienergetic but L-noncopectral as L-cospectral graphs are obviously L-equienergetic. We have devised a method to construct L-equienergetic graphs which are L-noncospectral.</description><identifier>ISSN: 0972-8600</identifier><identifier>EISSN: 2543-3474</identifier><identifier>DOI: 10.1016/j.akcej.2019.06.012</identifier><language>eng</language><publisher>Taylor & Francis</publisher><subject>Eigenvalue ; equienergetic ; graph energy ; spectrum</subject><ispartof>AKCE international journal of graphs and combinatorics, 2020-09, Vol.ahead-of-print (ahead-of-print), p.1-6</ispartof><rights>2020 The Author(s). Published with license by Taylor & Francis Group, LLC. 2020</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c365t-425318250d2c414ff7abd2f0077572bb52680ef1ecc330a7742005ceda18d9423</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.tandfonline.com/doi/pdf/10.1016/j.akcej.2019.06.012$$EPDF$$P50$$Ginformaworld$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.tandfonline.com/doi/full/10.1016/j.akcej.2019.06.012$$EHTML$$P50$$Ginformaworld$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27502,27924,27925,59143,59144</link.rule.ids></links><search><creatorcontrib>Vaidya, S. K.</creatorcontrib><creatorcontrib>Popat, Kalpesh M.</creatorcontrib><title>Construction of L-equienergetic graphs using some graph operations</title><title>AKCE international journal of graphs and combinatorics</title><description>For a graph G with n vertices and m edges, the eigenvalues of its adjacency matrix A(G) are known as eigenvalues of G. The sum of absolute values of eigenvalues of G is called the energy of G. The Laplacian matrix of G is defined as
where D(G) is the diagonal matrix with
entry is the degree of vertex v
i
. The collection of eigenvalues of L(G) with their multiplicities is called spectra of L(G). If
are the eigenvalues of L(G) then the Laplacian energy LE(G) of G is defined as
It is always interesting and challenging as well to investigate the graphs which are L-equienergetic but L-noncopectral as L-cospectral graphs are obviously L-equienergetic. We have devised a method to construct L-equienergetic graphs which are L-noncospectral.</description><subject>Eigenvalue</subject><subject>equienergetic</subject><subject>graph energy</subject><subject>spectrum</subject><issn>0972-8600</issn><issn>2543-3474</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>0YH</sourceid><sourceid>DOA</sourceid><recordid>eNp9kM1KAzEURoMoWLRP4GZeYMab_8xG0OJPoeBG1yGTScbU6aQmU6Rv77QVl64ufHAOl4PQDYYKAxa368p8WreuCOC6AlEBJmdoRjijJWWSnaMZ1JKUSgBconnOoQEsqSI1ETP0sIhDHtPOjiEORfTFqnRfu-AGlzo3Blt0yWw_crHLYeiKHDfutBRx65I5QPkaXXjTZzf_vVfo_enxbfFSrl6fl4v7VWmp4GPJCKdYEQ4tsQwz76VpWuIBpOSSNA0nQoHz2FlLKRgpGQHg1rUGq7ZmhF6h5cnbRrPW2xQ2Ju11NEEfh5g6bdL0cu8045NB1IZgpxifujBlW6kEt0apVtWTi55cNsWck_N_Pgz6UFWv9bGqPlTVIPRUdaLuTlQYfEwb8x1T3-rR7PuYfDKDDVnT_wQ_EX-AeQ</recordid><startdate>20200901</startdate><enddate>20200901</enddate><creator>Vaidya, S. K.</creator><creator>Popat, Kalpesh M.</creator><general>Taylor & Francis</general><general>Taylor & Francis Group</general><scope>0YH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>DOA</scope></search><sort><creationdate>20200901</creationdate><title>Construction of L-equienergetic graphs using some graph operations</title><author>Vaidya, S. K. ; Popat, Kalpesh M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c365t-425318250d2c414ff7abd2f0077572bb52680ef1ecc330a7742005ceda18d9423</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Eigenvalue</topic><topic>equienergetic</topic><topic>graph energy</topic><topic>spectrum</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Vaidya, S. K.</creatorcontrib><creatorcontrib>Popat, Kalpesh M.</creatorcontrib><collection>Taylor & Francis Open Access</collection><collection>CrossRef</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>AKCE international journal of graphs and combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Vaidya, S. K.</au><au>Popat, Kalpesh M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Construction of L-equienergetic graphs using some graph operations</atitle><jtitle>AKCE international journal of graphs and combinatorics</jtitle><date>2020-09-01</date><risdate>2020</risdate><volume>ahead-of-print</volume><issue>ahead-of-print</issue><spage>1</spage><epage>6</epage><pages>1-6</pages><issn>0972-8600</issn><eissn>2543-3474</eissn><abstract>For a graph G with n vertices and m edges, the eigenvalues of its adjacency matrix A(G) are known as eigenvalues of G. The sum of absolute values of eigenvalues of G is called the energy of G. The Laplacian matrix of G is defined as
where D(G) is the diagonal matrix with
entry is the degree of vertex v
i
. The collection of eigenvalues of L(G) with their multiplicities is called spectra of L(G). If
are the eigenvalues of L(G) then the Laplacian energy LE(G) of G is defined as
It is always interesting and challenging as well to investigate the graphs which are L-equienergetic but L-noncopectral as L-cospectral graphs are obviously L-equienergetic. We have devised a method to construct L-equienergetic graphs which are L-noncospectral.</abstract><pub>Taylor & Francis</pub><doi>10.1016/j.akcej.2019.06.012</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| issn | 0972-8600 2543-3474 |
| language | eng |
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| source | Taylor & Francis Open Access |
| subjects | Eigenvalue equienergetic graph energy spectrum |
| title | Construction of L-equienergetic graphs using some graph operations |
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