Exact double domination in the generalized Sierpinski graphs

Articles in Press

Document Type : Original Article

Authors

Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran

Abstract

A subset $D$ of vertices of a simple graph ‎$‎G‎$ ‎is ‎an exact double dominating set if each vertex $v$ of $G$ is dominated by exactly two vertices of $D$‎, ‎i.e. $|N_G[v]\cap D|=2$‎, ‎in ‎which ‎‎$‎N_G[v]‎$ ‎is ‎the closed neighborhood of $v$ in ‎$‎G‎$‎.‎ The generalized Sierpi'{n}ski graph $S(G,t)$ is a fractal-like graph that uses $G$ as a building block and can be constructed recursively in ‎$‎t‎$ ‎steps ‎from the base graph $G$. ‎In this paper we study and determine the existence of exact double dominating sets in generalized Sierpi'nski graphs $S(P_n,t)$‎, ‎$S(C_n,t)$‎, ‎$S(K_{1,n},t)$ and $S(K_n,t)$‎.

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AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 23 December 2024

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