The week's pick
Reseach Article
The Minimum Monopoly Distance Energy of a Graph
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 128 - Number 3 |
| Year of Publication: 2015 |
| Authors: Ahmed Mohammed Naji, N.D. Soner |
10.5120/ijca2015906457
|
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
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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