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.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

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://www.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://www.numdam.org/articles/10.1051/ro/2018074/

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