# THE IDENTIFYING CODE NUMBER AND FUNCTIGRAPHS

Document Type : Original Manuscript

Authors

Department of Mathematics, Imam Khomeini International University, P.O. Box 3414896818, Qazvin, Iran.

Abstract

Let G = (V (G); E(G)) be a simple graph. A set D of vertices G is an identifying code of G; if for every two vertices x and y the sets N_G[x] \ D and N_G[y] \ D are non- empty and different. The minimum cardinality of an identifying code in graph G is the identifying code number of G and it is denoted by gamma ID(G): Two vertices x and y are twin, when N_G[x] = N_G[y]: Graphs with at least two twin vertices are not identifiable graphs. In this paper, we deal with identifying code number of functigraph of G: Two upper bounds on identifying code number of functigraph are given. Also, we present some graph G with identifying code number |V (G)| - 2.

Keywords

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