TY - JOUR ID - 2328 TI - THE IDENTIFYING CODE NUMBER AND FUNCTIGRAPHS JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Shaminejad, A. AU - Vatandoost, E. AD - Department of Mathematics, Imam Khomeini International University, P.O. Box 3414896818, Qazvin, Iran. Y1 - 2022 PY - 2022 VL - 10 IS - 1 SP - 155 EP - 166 KW - Idenntifying code KW - identifiable graph KW - functigraph DO - 10.22044/jas.2021.9902.1487 N2 - 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. UR - https://jas.shahroodut.ac.ir/article_2328.html L1 - https://jas.shahroodut.ac.ir/article_2328_b6b4916c4606961fbc5985284ebb2ce2.pdf ER -