The Modified Negative Decision Number in Graphs
A mapping x:V→{-1,1} is called negative if ∑u∈N[v]x(u)≤1 for every v∈V. The maximum of the values of ∑v∈Vx(v) taken over all negative mappings x, is called the modified negative decision number and is denoted by βD′(G). In this paper, several sharp upper bounds of this number for a general graph are...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/135481 |
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| _version_ | 1849387199464734720 |
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| author | Changping Wang |
| author_facet | Changping Wang |
| author_sort | Changping Wang |
| collection | DOAJ |
| description | A mapping x:V→{-1,1} is called negative if ∑u∈N[v]x(u)≤1 for every v∈V. The maximum of the values of ∑v∈Vx(v) taken over all negative mappings x, is called the modified negative decision number and is denoted by βD′(G). In this paper, several sharp upper bounds of this number for a general graph are presented. Exact values of these numbers for cycles, paths, cliques and bicliques are found. |
| format | Article |
| id | doaj-art-2bf1fbcca67341d19a4c5189bae4bec9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2bf1fbcca67341d19a4c5189bae4bec92025-08-20T03:55:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/135481135481The Modified Negative Decision Number in GraphsChangping Wang0Department of Mathematics, Ryerson University, Toronto, ON, M5B 2K3, CanadaA mapping x:V→{-1,1} is called negative if ∑u∈N[v]x(u)≤1 for every v∈V. The maximum of the values of ∑v∈Vx(v) taken over all negative mappings x, is called the modified negative decision number and is denoted by βD′(G). In this paper, several sharp upper bounds of this number for a general graph are presented. Exact values of these numbers for cycles, paths, cliques and bicliques are found.http://dx.doi.org/10.1155/2011/135481 |
| spellingShingle | Changping Wang The Modified Negative Decision Number in Graphs International Journal of Mathematics and Mathematical Sciences |
| title | The Modified Negative Decision Number in Graphs |
| title_full | The Modified Negative Decision Number in Graphs |
| title_fullStr | The Modified Negative Decision Number in Graphs |
| title_full_unstemmed | The Modified Negative Decision Number in Graphs |
| title_short | The Modified Negative Decision Number in Graphs |
| title_sort | modified negative decision number in graphs |
| url | http://dx.doi.org/10.1155/2011/135481 |
| work_keys_str_mv | AT changpingwang themodifiednegativedecisionnumberingraphs AT changpingwang modifiednegativedecisionnumberingraphs |