1 research outputs found
One size resolvability of graphs
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