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The Average Lower Independence Number Of Total Graphs
Authors: Aysun Ayatac and Tufan Turaci
Number of views: 463
In communication networks, "vulnerability" indicates the resistance of
a network to disruptions in communication after a breakdown of some pro-
cessors or communication links. We may use graphs to model networks,
as graph theoretical parameters can be used to describe the stability and
reliability of communication networks If we think of a graph as model-
ing a network, the average lower independence number of a graph is one
measure of graph vulnerability. For a vertex v of a graph G = (V;E),
the lower independence number iv(G) of G relative to v is the minimum
cardinality of a maximal independent set of G that contains v. The av-
erage lower independence number of G, denoted by iav(G), is the value
iav(G) = 1
jV (G)j
P
v²V (G) iv(G). In this paper, we de¯ned and examined
this parameter and considered the average lower independence number of
special graphs and theirs total graphs.