Domination integrity of some graph classes

Besirik, Ayse; Kilic, Elgin

doi:10.1051/ro/2018074

Besirik, Ayse ¹ ; Kilic, Elgin ¹

RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1721-1728.

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Résumé

The stability of a communication network has a great importance in network design. There are several vulnerability measures used to determine the resistance of network to the disruption in this sense. Domination theory provides a model to measure the vulnerability of a graph network. A new vulnerability measure of domination integrity was introduced by Sundareswaran in his Ph.D. thesis (Parameters of vulnerability in graphs (2010)) and defined as $DI (G) = min {| S | + m (G - S) : S \in V (G)}$ where $m (G - S)$ denotes the order of a largest component of graph $G - S$ and $S$ is a dominating set of $G$ . The domination integrity of an undirected connected graph is such a measure that works on the whole graph and also the remaining components of graph after any break down. Here we determine the domination integrity of wheel graph $W_{1, n,}$ , Ladder graph $L_{n}$ , $S_{m, n}$ , Friendship graph $F_{n}$ , Thorn graph of $P_{n}$ and $C_{n}$ which are commonly used graph models in network design.

MR Zbl

DOI : 10.1051/ro/2018074

Classification : 05C12, 05C35, 05C69, 68R10
Mots-clés : Integrity, domination, domination integrity

Affiliations des auteurs :

Besirik, Ayse ¹ ; Kilic, Elgin ¹

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     author = {Besirik, Ayse and Kilic, Elgin},
     title = {Domination integrity of some graph classes},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1721--1728},
     publisher = {EDP-Sciences},
     volume = {53},
     number = {5},
     year = {2019},
     doi = {10.1051/ro/2018074},
     zbl = {1430.05025},
     mrnumber = {4016524},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro/2018074/}
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Besirik, Ayse; Kilic, Elgin. Domination integrity of some graph classes. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1721-1728. doi : 10.1051/ro/2018074. http://archive.numdam.org/articles/10.1051/ro/2018074/

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