On Cycle Related Graphs with Constant Metric Dimension
نویسندگان
چکیده
If is a connected graph, the distance between two vertices G , d u v , u v V G G is the length of a shortest path between them. Let be an ordered set of vertices of and let v be a vertex of . The representation 1 2 = , , , k W w w w G r v W of v with respect to is the -tuple W k 1 2 , , d v w , , , k d v w d v w , . If distinct vertices of have distinct representations with respect to , then is called a resolving set or locating set for . A resolving set of minimum cardinality is called a basis for and this cardinality is the metric dimension of , denoted by . A family of connected graphs is a family with constant metric dimension if is finite and does not depend upon the choice of in . In this paper, we show that dragon graph denoted by and the graph obtained from prism denoted by have constant metric dimension. G W k k C x W G G G , n m m G di G 2 dim G T k y
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تاریخ انتشار 2013