On exponential domination and graph operations

Document Type: Research Paper

Authors

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

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