TY - JOUR
ID - 2767
TI - On exponential domination and graph operations
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Atay, Betul
AU - Aytac, Aysun
AD - Department of Computer and Inst. Tech. Edu., Faculty of Education, Agri Ibrahim Cecen University, Agri, Turkey
AD - Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova-Izmir, Turkey
Y1 - 2017
PY - 2017
VL - 8
IS - 2
SP - 243
EP - 250
KW - Graph vulnerability
KW - network design and communication
KW - exponential domination number
KW - edge corona
KW - neighbourhood corona
DO - 10.22075/ijnaa.2017.3056.1494
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_2767.html
L1 - https://ijnaa.semnan.ac.ir/article_2767_30d3be476f5e7e4708605bbc92f6406d.pdf
ER -