On exponential domination and graph operations | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 21، دوره 8، شماره 2، 2017، صفحه 243-250 اصل مقاله (363.57 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2017.3056.1494 | ||
| نویسندگان | ||
| Betul Atay1؛ Aysun Aytac* 2 | ||
| 1Department of Computer and Inst. Tech. Edu., Faculty of Education, Agri Ibrahim Cecen University, Agri, Turkey | ||
| 2Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova-Izmir, Turkey | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Graph vulnerability؛ network design and communication؛ exponential domination number؛ edge corona؛ neighbourhood corona | ||
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