Complete multipartite graphs that are determined, up to switching, by their Seidel spectrum
It is known that complete multipartite graphs are determined by their distance spectrum but not by their adjacency spectrum. The Seidel spectrum of a graph G on more than one vertex does not determine the graph, since any graph obtained from G by Seidel switching has the same Seidel spectrum. We con...
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| Veröffentlicht in: | Linear algebra and its applications 2019-03, Vol.564, p.58-71 |
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| creator | Berman, Abraham Shaked-Monderer, Naomi Singh, Ranveer Zhang, Xiao-Dong |
| description | It is known that complete multipartite graphs are determined by their distance spectrum but not by their adjacency spectrum. The Seidel spectrum of a graph G on more than one vertex does not determine the graph, since any graph obtained from G by Seidel switching has the same Seidel spectrum. We consider G to be determined by its Seidel spectrum, up to switching, if any graph with the same spectrum is switching equivalent to a graph isomorphic to G. It is shown that any graph which has the same spectrum as a complete k-partite graph is switching equivalent to a complete k-partite graph, and if the different partition sets sizes are p1,…,pl, and there are at least three partition sets of each size pi, i=1,…,l, then G is determined, up to switching, by its Seidel spectrum. Sufficient conditions for a complete tripartite graph to be determined by its Seidel spectrum are discussed. |
| doi_str_mv | 10.1016/j.laa.2018.11.022 |
| format | Article |
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The Seidel spectrum of a graph G on more than one vertex does not determine the graph, since any graph obtained from G by Seidel switching has the same Seidel spectrum. We consider G to be determined by its Seidel spectrum, up to switching, if any graph with the same spectrum is switching equivalent to a graph isomorphic to G. It is shown that any graph which has the same spectrum as a complete k-partite graph is switching equivalent to a complete k-partite graph, and if the different partition sets sizes are p1,…,pl, and there are at least three partition sets of each size pi, i=1,…,l, then G is determined, up to switching, by its Seidel spectrum. 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Sufficient conditions for a complete tripartite graph to be determined by its Seidel spectrum are discussed.</description><subject>Complete multipartite graphs</subject><subject>Equivalence</subject><subject>Graphs</subject><subject>Linear algebra</subject><subject>Partitions (mathematics)</subject><subject>S-determined</subject><subject>Seidel matrix</subject><subject>Seidel switching</subject><subject>Switching</subject><issn>0024-3795</issn><issn>1873-1856</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKxDAUhoMoOI4-gLuA22nNSS9pcSWDNxhwoa5chDQ5ncnQTmuSKvP2ZhjXLsIh8P3n8hFyDSwFBuXtNu2USjmDKgVIGecnZAaVyBKoivKUzBjjeZKJujgnF95vGWO5YHxGPpdDP3YYkPZTF-yoXLDxs3Zq3HgaNipQ5ZCaSLje7tAs6DTSMFD_Y4Pe2N16QZt9BNE6-obWYEf9iDq4qb8kZ63qPF791Tn5eHx4Xz4nq9enl-X9KtFZWYWkakUbX62K3LRMIGYqL3hZF41h2GjQquWN0TVHA41oAQWIEg1C3uSZLupsTm6OfUc3fE3og9wOk9vFkZJHB4WAIq8iBUdKu8F7h60cne2V20tg8uBQbmV0KA8OJYCMDmPm7pjBuP63RSe9trjTaKyLN0oz2H_SvxZwewU</recordid><startdate>20190301</startdate><enddate>20190301</enddate><creator>Berman, Abraham</creator><creator>Shaked-Monderer, Naomi</creator><creator>Singh, Ranveer</creator><creator>Zhang, Xiao-Dong</creator><general>Elsevier Inc</general><general>American Elsevier Company, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-0783-051X</orcidid></search><sort><creationdate>20190301</creationdate><title>Complete multipartite graphs that are determined, up to switching, by their Seidel spectrum</title><author>Berman, Abraham ; Shaked-Monderer, Naomi ; Singh, Ranveer ; Zhang, Xiao-Dong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c368t-8f7f8f79a54df07ee3a452695bd0ebc1caf2bdc92ed1b7f1e7176ede14b43c593</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Complete multipartite graphs</topic><topic>Equivalence</topic><topic>Graphs</topic><topic>Linear algebra</topic><topic>Partitions (mathematics)</topic><topic>S-determined</topic><topic>Seidel matrix</topic><topic>Seidel switching</topic><topic>Switching</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Berman, Abraham</creatorcontrib><creatorcontrib>Shaked-Monderer, Naomi</creatorcontrib><creatorcontrib>Singh, Ranveer</creatorcontrib><creatorcontrib>Zhang, Xiao-Dong</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Linear algebra and its applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Berman, Abraham</au><au>Shaked-Monderer, Naomi</au><au>Singh, Ranveer</au><au>Zhang, Xiao-Dong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Complete multipartite graphs that are determined, up to switching, by their Seidel spectrum</atitle><jtitle>Linear algebra and its applications</jtitle><date>2019-03-01</date><risdate>2019</risdate><volume>564</volume><spage>58</spage><epage>71</epage><pages>58-71</pages><issn>0024-3795</issn><eissn>1873-1856</eissn><abstract>It is known that complete multipartite graphs are determined by their distance spectrum but not by their adjacency spectrum. The Seidel spectrum of a graph G on more than one vertex does not determine the graph, since any graph obtained from G by Seidel switching has the same Seidel spectrum. We consider G to be determined by its Seidel spectrum, up to switching, if any graph with the same spectrum is switching equivalent to a graph isomorphic to G. It is shown that any graph which has the same spectrum as a complete k-partite graph is switching equivalent to a complete k-partite graph, and if the different partition sets sizes are p1,…,pl, and there are at least three partition sets of each size pi, i=1,…,l, then G is determined, up to switching, by its Seidel spectrum. Sufficient conditions for a complete tripartite graph to be determined by its Seidel spectrum are discussed.</abstract><cop>Amsterdam</cop><pub>Elsevier Inc</pub><doi>10.1016/j.laa.2018.11.022</doi><tpages>14</tpages><orcidid>https://orcid.org/0000-0003-0783-051X</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | Linear algebra and its applications, 2019-03, Vol.564, p.58-71 |
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| language | eng |
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| source | ScienceDirect Journals (5 years ago - present); EZB-FREE-00999 freely available EZB journals |
| subjects | Complete multipartite graphs Equivalence Graphs Linear algebra Partitions (mathematics) S-determined Seidel matrix Seidel switching Switching |
| title | Complete multipartite graphs that are determined, up to switching, by their Seidel spectrum |
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