Volume 53, Number 1, January–March 2019
|Page(s)||261 - 268|
|Published online||15 February 2019|
Average covering number for some graphs
Arts and Science Faculty, Manisa Celal Bayar University, 45140 Manisa, Turkey
* Corresponding author: email@example.com
Accepted: 21 May 2018
The interconnection networks are modeled by means of graphs to determine the reliability and vulnerability. There are lots of parameters that are used to determine vulnerability. The average covering number is one of them which is denoted by , where G is simple, connected and undirected graph of order n ≥ 2. In a graph G = (V(G), E(G)) a subset of vertices is called a cover set of G with respect to v or a local covering set of vertex v, if each edge of the graph is incident to at least one vertex of Sv. The local covering number with respect to v is the minimum cardinality of among the Sv sets and denoted by βv. The average covering number of a graph G is defined as In this paper, the average covering numbers of kth power of a cycle and Pn □ Pm, Pn □ Cm, cartesian product of Pn and Pm, cartesian product of Pn and Cm are given, respectively.
Mathematics Subject Classification: 68R10 / 05C76 / 05C70
Key words: Graph theory / graph operations / covering
© EDP Sciences, ROADEF, SMAI 2019
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