Variable neighborhood search for extremal graphs. 16. Some conjectures related to the largest eigenvalue of a graph
We consider four conjectures related to the largest eigenvalue of (the adjacency matrix of) a graph (i.e., to the index of the graph). Three of them have been formulated after some experiments with the programming system AutoGraphiX, designed for finding extremal graphs with respect to given propert...
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| Veröffentlicht in: | European journal of operational research 2008-12, Vol.191 (3), p.661-676 |
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| container_title | European journal of operational research |
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| creator | Aouchiche, M. Bell, F.K. Cvetković, D. Hansen, P. Rowlinson, P. Simić, S.K. Stevanović, D. |
| description | We consider four conjectures related to the largest eigenvalue of (the adjacency matrix of) a graph (i.e., to the index of the graph). Three of them have been formulated after some experiments with the programming system AutoGraphiX, designed for finding extremal graphs with respect to given properties by the use of variable neighborhood search. The conjectures are related to the maximal value of the irregularity and spectral spread in
n-vertex graphs, to a Nordhaus–Gaddum type upper bound for the index, and to the maximal value of the index for graphs with given numbers of vertices and edges. None of the conjectures has been resolved so far. We present partial results and provide some indications that the conjectures are very hard. |
| doi_str_mv | 10.1016/j.ejor.2006.12.059 |
| format | Article |
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n-vertex graphs, to a Nordhaus–Gaddum type upper bound for the index, and to the maximal value of the index for graphs with given numbers of vertices and edges. None of the conjectures has been resolved so far. We present partial results and provide some indications that the conjectures are very hard.</description><identifier>ISSN: 0377-2217</identifier><identifier>EISSN: 1872-6860</identifier><identifier>DOI: 10.1016/j.ejor.2006.12.059</identifier><identifier>CODEN: EJORDT</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Adjacency matrix ; Applied sciences ; AutoGraphiX ; Computer science; control theory; systems ; Conjectures ; Eigenvalues ; Exact sciences and technology ; Extremal graph ; Graph ; Graph theory ; Graphs ; Index ; Information retrieval. Graph ; Irregularity ; Largest eigenvalue ; Optimization algorithms ; Spectral spread ; Studies ; Theoretical computing ; Variable neighborhood search</subject><ispartof>European journal of operational research, 2008-12, Vol.191 (3), p.661-676</ispartof><rights>2007 Elsevier B.V.</rights><rights>2008 INIST-CNRS</rights><rights>Copyright Elsevier Sequoia S.A. Dec 16, 2008</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c425t-9ae556889afe23381dac9a58a9e1ef087359aedce9ff5b629901d3098c4508e23</citedby><cites>FETCH-LOGICAL-c425t-9ae556889afe23381dac9a58a9e1ef087359aedce9ff5b629901d3098c4508e23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.ejor.2006.12.059$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>309,310,314,776,780,785,786,3536,3993,23910,23911,25119,27903,27904,45974</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20452983$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/eeeejores/v_3a191_3ay_3a2008_3ai_3a3_3ap_3a661-676.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>Aouchiche, M.</creatorcontrib><creatorcontrib>Bell, F.K.</creatorcontrib><creatorcontrib>Cvetković, D.</creatorcontrib><creatorcontrib>Hansen, P.</creatorcontrib><creatorcontrib>Rowlinson, P.</creatorcontrib><creatorcontrib>Simić, S.K.</creatorcontrib><creatorcontrib>Stevanović, D.</creatorcontrib><title>Variable neighborhood search for extremal graphs. 16. Some conjectures related to the largest eigenvalue of a graph</title><title>European journal of operational research</title><description>We consider four conjectures related to the largest eigenvalue of (the adjacency matrix of) a graph (i.e., to the index of the graph). Three of them have been formulated after some experiments with the programming system AutoGraphiX, designed for finding extremal graphs with respect to given properties by the use of variable neighborhood search. The conjectures are related to the maximal value of the irregularity and spectral spread in
n-vertex graphs, to a Nordhaus–Gaddum type upper bound for the index, and to the maximal value of the index for graphs with given numbers of vertices and edges. None of the conjectures has been resolved so far. We present partial results and provide some indications that the conjectures are very hard.</description><subject>Adjacency matrix</subject><subject>Applied sciences</subject><subject>AutoGraphiX</subject><subject>Computer science; control theory; systems</subject><subject>Conjectures</subject><subject>Eigenvalues</subject><subject>Exact sciences and technology</subject><subject>Extremal graph</subject><subject>Graph</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Index</subject><subject>Information retrieval. 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Some conjectures related to the largest eigenvalue of a graph</title><author>Aouchiche, M. ; Bell, F.K. ; Cvetković, D. ; Hansen, P. ; Rowlinson, P. ; Simić, S.K. ; Stevanović, D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c425t-9ae556889afe23381dac9a58a9e1ef087359aedce9ff5b629901d3098c4508e23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Adjacency matrix</topic><topic>Applied sciences</topic><topic>AutoGraphiX</topic><topic>Computer science; control theory; systems</topic><topic>Conjectures</topic><topic>Eigenvalues</topic><topic>Exact sciences and technology</topic><topic>Extremal graph</topic><topic>Graph</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Index</topic><topic>Information retrieval. 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Some conjectures related to the largest eigenvalue of a graph</atitle><jtitle>European journal of operational research</jtitle><date>2008-12-16</date><risdate>2008</risdate><volume>191</volume><issue>3</issue><spage>661</spage><epage>676</epage><pages>661-676</pages><issn>0377-2217</issn><eissn>1872-6860</eissn><coden>EJORDT</coden><abstract>We consider four conjectures related to the largest eigenvalue of (the adjacency matrix of) a graph (i.e., to the index of the graph). Three of them have been formulated after some experiments with the programming system AutoGraphiX, designed for finding extremal graphs with respect to given properties by the use of variable neighborhood search. The conjectures are related to the maximal value of the irregularity and spectral spread in
n-vertex graphs, to a Nordhaus–Gaddum type upper bound for the index, and to the maximal value of the index for graphs with given numbers of vertices and edges. None of the conjectures has been resolved so far. We present partial results and provide some indications that the conjectures are very hard.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.ejor.2006.12.059</doi><tpages>16</tpages></addata></record> |
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| source | RePEc; Elsevier ScienceDirect Journals |
| subjects | Adjacency matrix Applied sciences AutoGraphiX Computer science control theory systems Conjectures Eigenvalues Exact sciences and technology Extremal graph Graph Graph theory Graphs Index Information retrieval. Graph Irregularity Largest eigenvalue Optimization algorithms Spectral spread Studies Theoretical computing Variable neighborhood search |
| title | Variable neighborhood search for extremal graphs. 16. Some conjectures related to the largest eigenvalue of a graph |
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