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...

Full description

Saved in:
Bibliographic Details
Main Author: Changping Wang
Format: Article
Language:English
Published: Wiley 2011-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2011/135481
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849387199464734720
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