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

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)

‎.

Keywords

Main Subjects