One size resolvability of graphs

• Author(s): Kwancharone, S. ; Saenpholphat, V. ; Fonseca, C. M. da
• Date: 2008
• Persistent ID: http://hdl.handle.net/10316/11260
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Resolving set; One size resolving set
• Document Type: Preprint
• Language: English

Description

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.