On Vulnerability Of The Hexagonal Cactus Chains

TUFAN TURACI

Abstract


Let G(V(G),E(G)) be a simple molecular graph without directed and multiple edges and without loops. The vulnerability value of a graph shows the resistance of the network after the disruption of some centers or connection lines until a communication breakdown. The domination number and its variations are the most important vulnerability parameters for graphs. One of them is the average lower domination number. It is denoted by , also is defined as: , where the lower domination number, denoted by , is the minimum cardinality of a dominating set of the graph G that contains the vertex (Henning 2004). In this paper, the average lower domination number of different hexagonal cactus chains are determined. 


Keywords


Graph Vulnerability, Domination number, Average lower domination number, Hexagonal cactus chains.

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DOI: http://dx.doi.org/10.7212%2Fzkufbd.v8i1.829

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