کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4648187 | 1342397 | 2012 | 8 صفحه PDF | دانلود رایگان |

For a set WW of vertices and a vertex vv in a connected graph GG, the kk-vector rW(v)=(d(v,w1),…,d(v,wk))rW(v)=(d(v,w1),…,d(v,wk)) is the metric representation of vv with respect to WW, where W={w1,…,wk}W={w1,…,wk} and d(x,y)d(x,y) is the distance between the vertices xx and yy. The set WW is a resolving set for GG if distinct vertices of GG have distinct metric representations with respect to WW. The minimum cardinality of a resolving set for GG is its metric dimension . In this paper, we study the metric dimension of the lexicographic product of graphs GG and HH, denoted by G[H]G[H]. First, we introduce a new parameter, the adjacency dimension , of a graph. Then we obtain the metric dimension of G[H]G[H] in terms of the order of GG and the adjacency dimension of HH.
Journal: Discrete Mathematics - Volume 312, Issue 22, 28 November 2012, Pages 3349–3356