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Title: One size resolvability of graphs
Authors: Kwancharone, S. 
Saenpholphat, V. 
Fonseca, C. M. da 
Keywords: Resolving set; One size resolving set
Issue Date: 2008
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 08-17 (2008)
Abstract: For an ordered set W = {w1,w2, · · · ,wk} of vertices in a connected graph G and a vertex v of G, the code of v with respect to W is the k-vector CW(v) = (d(v,w1), d(v,w2), · · · , d(v,wk)). The set W is a one size resolving set for G if (1) the size of subgraph hWi induced by W is one and (2) distinct vertices of G have distinct code with respect to W. The minimum cardinality of a one size resolving set in graph G is the one size resolving number, denoted by or(G). A one size resolving set of cardinality or(G) is called an or-set of G. We study the existence of or-set in graphs and characterize all nontrivial connected graphs G of order n with or(G) = n and n − 1.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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