Path Resolvability in Graphs-A New Encryption Technique

The shortest distance between two vertices u and v in a connected graph G is the length of a shortest u−v path in G denoted byd(u, v). A subset W of a vertex set Vof G is a resolving set if each pair of distinct vertices u, v∈V(G) there is a vertex w∈V such that d u, w ≠d(v, w). A resolving set W is said to be a path resolving set if it is induces a path. The minimum cardinality of the resolving set W is said to be path resolving number. In resolvability the distinct vertex of a graph Ghas distinct code with respect to W meanwhile the code of a vertex is depend upon the resolving set W. The structural symmetry of a graph implies the same path number with different resolving sets. It can be used in the developing of the symmetric key cryptosystems. In this paper we encrypt secret messages over the web graph P_n×C_m using path resolving set.