Abstract:

       This paper presents two definitions for neighborhood restrictions labels of a graph, semitotal neighborhood restrictions label SN(p,q) and total neighborhood restrictions label TN(p,q).SN(p,q) is a normal label that only restricts the neighborhood of part dots.TN(p,q) is a normal label that restricts the neighborhood of all dots. Semitotal neighborhood restrictions label number and total neighborhood restrictions label number of a graph G are SL_p,q(G) and TL_p,q(G).This paper gives the bounds of SL_p,q(G) and TL_p,q(G) of some graphs.

Key words: semitotal neighborhood restrictions label, total neighborhood restrictions label, complete graph, bipartite graphs