The forwarding indices of graphs - a survey
A routing \(R\) of a connected graph \(G\) of order \(n\) is a collection of \(n(n-1)\) simple paths connecting every ordered pair of vertices of \(G\). The vertex-forwarding index \(\xi(G,R)\) of \(G\) with respect to a routing \(R\) is defined as the maximum number of paths in \(R\) passing throug...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2013-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol33/2/art/opuscula_math_3323.pdf |
| _version_ | 1819238670583988224 |
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| author | Jun-Ming Xu Min Xu |
| author_facet | Jun-Ming Xu Min Xu |
| author_sort | Jun-Ming Xu |
| collection | DOAJ |
| description | A routing \(R\) of a connected graph \(G\) of order \(n\) is a collection of \(n(n-1)\) simple paths connecting every ordered pair of vertices of \(G\). The vertex-forwarding index \(\xi(G,R)\) of \(G\) with respect to a routing \(R\) is defined as the maximum number of paths in \(R\) passing through any vertex of \(G\). The vertex-forwarding index \(\xi(G)\) of \(G\) is defined as the minimum \(\xi(G,R)\) over all routings \(R\) of \(G\). Similarly, the edge-forwarding index \(\pi(G,R)\) of \(G\) with respect to a routing \(R\) is the maximum number of paths in \(R\) passing through any edge of \(G\). The edge-forwarding index \(\pi(G)\) of \(G\) is the minimum \(\pi(G,R)\) over all routings \(R\) of \(G\). The vertex-forwarding index or the edge-forwarding index corresponds to the maximum load of the graph. Therefore, it is important to find routings minimizing these indices and thus has received much research attention for over twenty years. This paper surveys some known results on these forwarding indices, further research problems and several conjectures, also states some difficulty and relations to other topics in graph theory. |
| first_indexed | 2024-12-23T13:39:55Z |
| format | Article |
| id | doaj.art-b87b395b5d7c4d4fa2c7992eef3e5b95 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-23T13:39:55Z |
| publishDate | 2013-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-b87b395b5d7c4d4fa2c7992eef3e5b952022-12-21T17:44:53ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742013-01-01332345372http://dx.doi.org/10.7494/OpMath.2013.33.2.3453323The forwarding indices of graphs - a surveyJun-Ming Xu0Min Xu1University of Science and Technology of China, School of Mathematical Sciences, Wentsun Wu Key Laboratory of CAS, Hefei, Anhui, 230026, ChinaBeijing Normal University, School of Mathematical Sciences, Ministry of Education, Laboratory of Mathematics and Complex Systems, Beijing, 100875, ChinaA routing \(R\) of a connected graph \(G\) of order \(n\) is a collection of \(n(n-1)\) simple paths connecting every ordered pair of vertices of \(G\). The vertex-forwarding index \(\xi(G,R)\) of \(G\) with respect to a routing \(R\) is defined as the maximum number of paths in \(R\) passing through any vertex of \(G\). The vertex-forwarding index \(\xi(G)\) of \(G\) is defined as the minimum \(\xi(G,R)\) over all routings \(R\) of \(G\). Similarly, the edge-forwarding index \(\pi(G,R)\) of \(G\) with respect to a routing \(R\) is the maximum number of paths in \(R\) passing through any edge of \(G\). The edge-forwarding index \(\pi(G)\) of \(G\) is the minimum \(\pi(G,R)\) over all routings \(R\) of \(G\). The vertex-forwarding index or the edge-forwarding index corresponds to the maximum load of the graph. Therefore, it is important to find routings minimizing these indices and thus has received much research attention for over twenty years. This paper surveys some known results on these forwarding indices, further research problems and several conjectures, also states some difficulty and relations to other topics in graph theory.http://www.opuscula.agh.edu.pl/vol33/2/art/opuscula_math_3323.pdfgraph theoryvertex-forwarding indexedge-forwarding indexroutingnetworks |
| spellingShingle | Jun-Ming Xu Min Xu The forwarding indices of graphs - a survey Opuscula Mathematica graph theory vertex-forwarding index edge-forwarding index routing networks |
| title | The forwarding indices of graphs - a survey |
| title_full | The forwarding indices of graphs - a survey |
| title_fullStr | The forwarding indices of graphs - a survey |
| title_full_unstemmed | The forwarding indices of graphs - a survey |
| title_short | The forwarding indices of graphs - a survey |
| title_sort | forwarding indices of graphs a survey |
| topic | graph theory vertex-forwarding index edge-forwarding index routing networks |
| url | http://www.opuscula.agh.edu.pl/vol33/2/art/opuscula_math_3323.pdf |
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