Research Article
The Minimum Monopoly Distance Energy of a Graph
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 128 - Issue 3 |
| Published: October 2015 |
| Authors: Ahmed Mohammed Naji, N.D. Soner |
10.5120/ijca2015906457
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Ahmed Mohammed Naji, N.D. Soner . The Minimum Monopoly Distance Energy of a Graph. International Journal of Computer Applications. 128, 3 (October 2015), 1-6. DOI=10.5120/ijca2015906457
@article{ 10.5120/ijca2015906457,
author = { Ahmed Mohammed Naji,N.D. Soner },
title = { The Minimum Monopoly Distance Energy of a Graph },
journal = { International Journal of Computer Applications },
year = { 2015 },
volume = { 128 },
number = { 3 },
pages = { 1-6 },
doi = { 10.5120/ijca2015906457 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2015
%A Ahmed Mohammed Naji
%A N.D. Soner
%T The Minimum Monopoly Distance Energy of a Graph%T
%J International Journal of Computer Applications
%V 128
%N 3
%P 1-6
%R 10.5120/ijca2015906457
%I Foundation of Computer Science (FCS), NY, USA
Abstract
In a graph G = (V,E), a set M ⊆ V is called a monopoly set of G if every vertex v ∈ V - M has at least d(v)/2 neighbors in M. The monopoly size mo(G) of G is the minimum cardinality of a monopoly set among all monopoly sets in G. In this paper, the minimum monopoly distance energy EMd(G) of a connected graph G is introduced and minimum monopoly distance energies of some standard graphs are computed. Some properties of the characteristic polynomial of the minimum monopoly distance matrix of G are obtained. Finally. Upper and lower bounds for EMd(G) are established.
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