The edge hop domination number of a graph
Abstract
Let G = (V,E) be a graph. A set S ⊆ E(G) is called an edge hop dominating set if S=E(G) or for every g∈E(G)\S, there exists h∈S such that d(g,h) = 1. The minimum cardinality of an edge hop domination set of G is called the edge hop domination number of G is denoted by γeh(G). The edge hop domination number of some standard graphs are determined. It is proved that for any two connected graphs H and K of orders n1 and n2 respectively, γeh(H+K)=3. Also it is proved that for any two connected graphs of sizes m1≥3 and m2≥3 respectively, γeh(H◦K)≤m1.
Copyright © 2021 D. Anusha, S. Joseph Robin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
D. Anusha, S. J. Robin, The edge hop domination number of a graph, J. Math. Comput. Sci. 11 (2021), 7440–7452. https://doi.org/10.28919/jmcs/6577
BibTeX
@article{Anusha2021,
author = {Anusha, D. and Robin, S. Joseph},
title = {The edge hop domination number of a graph},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {7440--7452},
doi = {10.28919/jmcs/6577}
}