Global minus domination in graphs
A function $f:V(G)rightarrow {-1,0,1}$ is a {em minus dominating function} if for every vertex $vin V(G)$, $sum_{uin N[v]}f(u)ge 1$. A minus dominating function $f$ of $G$ is called a {em global minus dominating function} if $f$ is also a minus dominating function of the complement $overline{G}$...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Isfahan
2014-06-01
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| Series: | Transactions on Combinatorics |
| Subjects: | |
| Online Access: | http://www.combinatorics.ir/pdf_4989_5b88a1a5cbb3252ba0dbaab4aeb314b6.html |
| Summary: | A function $f:V(G)rightarrow {-1,0,1}$ is a {em minus
dominating function} if for every vertex $vin V(G)$, $sum_{uin
N[v]}f(u)ge 1$. A minus dominating function $f$ of $G$ is called
a {em global minus dominating function} if $f$ is also a minus
dominating function of the complement $overline{G}$ of $G$. The
{em global minus domination number} $gamma_{g}^-(G)$ of $G$ is
defined as $gamma_{g}^-(G)=min{sum_{vin V(G)} f(v)mid f
mbox{ is a global minus dominating function of } G}$. In this
paper we initiate the study of global minus domination number in
graphs and we establish lower and upper bounds for the global
minus domination number. |
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| ISSN: | 2251-8657 2251-8665 |