Title : ( Distribution of global defensive k-alliances over some graph products )
Authors: Mostafa Tavakoli , Sandi Klavžar ,
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Abstract
If G = (VG , EG ) is a graph, then S ⊆ VG is a global defensive k-alliance in G if (i) each vertex not in S has a neighbor in S and (ii) each vertex of S has at least k more neighbors inside S than outside of it. The global defensive k-alliance number of G is the minimum cardinality among all global defensive k-alliance in G. In this paper this concept is studied on the generalized hierarchical, the lexicographic, the corona, and the edge corona product. For all of these products upper bounds expressed with related invariants of the factors are given. Sharpness of the bounds is also discussed.
Keywords
, Global alliance, Global defensive k-alliance, Hierarchical product of graphs, Lexicographic product of graphs
@article{paperid:1074710,
author = {Tavakoli, Mostafa and Sandi Klavžar},
title = {Distribution of global defensive k-alliances over some graph products},
journal = {Central European Journal of Operations Research},
year = {2019},
volume = {27},
number = {3},
month = {September},
issn = {1435-246X},
pages = {615--623},
numpages = {8},
keywords = {Global alliance; Global defensive k-alliance; Hierarchical product of graphs;Lexicographic product of graphs},
}
%0 Journal Article
%T Distribution of global defensive k-alliances over some graph products
%A Tavakoli, Mostafa
%A Sandi Klavžar
%J Central European Journal of Operations Research
%@ 1435-246X
%D 2019
