Browsing by Publisher "Science Society of Thailand under Royal Patronage"

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    Neighbour isolated scattering number of graphs
    (Science Society of Thailand under Royal Patronage, 2015) Aslan E.
    The scattering number is a measure of the vulnerability of a graph. In this paper we investigate a refinement that involves the neighbour isolated version of the parameter. The neighbour isolated scattering number of a noncomplete graph G is defined tobe NIS(G) = max{i(G/X)-|X|: i(G/X) ≥ 1} where the maximum is taken over all X, the cut strategy of G, and i(G/X) is the number of components which are isolated vertices of G/X. Like the scattering number itself, this is a measure of the vulnerability of a graph, but it is more sensitive. The relations between neighbour isolated scattering number and other parameters are determined and the neighbour isolated scattering number of trees and other families are obtained. We also give some results for the neighbour isolated scattering number of the graphs obtained by some graph operations.
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    The average binding number of graphs
    (Science Society of Thailand under Royal Patronage, 2019) Aslan E.
    The binding number is a measure of the vulnerability of a graph. We investigate a refinement that involves the average of this parameter. Like the binding number itself, the average binding number bindav(G) of G measures the vulnerability of a graph, which is more sensitive. In this study, some bounds of the average binding number of some special graphs are obtained. Furthermore some results about the average binding number of graphs obtained from graph operations are also provided. © 2018 Science Society of Thailand under Royal Patronage. All rights reserved.