On exponential domination and graph operations

Atay, Betul; Aytac, Aysun

doi:10.22075/ijnaa.2017.3056.1494

On exponential domination and graph operations

Document Type : Research Paper

Authors

Betul Atay ¹

Aysun Aytac ²

¹ Department of Computer and Inst. Tech. Edu., Faculty of Education, Agri Ibrahim Cecen University, Agri, Turkey

² Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova-Izmir, Turkey

10.22075/ijnaa.2017.3056.1494

Abstract

An exponential dominating set of graph $G = (V,E )$ is a subset $S\subseteq V(G)$ such that $\sum_{u\in S}(1/2)^{\overline{d}{(u,v)-1}}\geq 1$ for every vertex $v$ in $V(G)-S$, where $\overline{d}(u,v)$ is the distance between vertices $u \in S$ and $v \in V(G)-S$ in the graph $G -(S-\{u\})$. The exponential domination number, $\gamma_{e}(G)$, is the smallest cardinality of an exponential dominating set. Graph operations are important methods for constructing new graphs, and they play key roles in the design and analysis of networks. In this study, we consider the exponential domination number of graph operations including edge corona, neighborhood corona and power.

Keywords

Graph vulnerability

network design and communication

exponential domination number

edge corona

neighbourhood corona