tailieunhanh - Some results and examples on difference cordial graphs

In this paper we introduce some results on difference cordial graphs and describe the difference cordial labeling for some families of graphs. | Turk J Math (2016) 40: 417 – 427 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Some results and examples on difference cordial graphs 1 Mohammed SEOUD1 , Shakir SALMAN1,2,∗ Department of Mathematics, Faculty of Science, Ain Shams University, Abbasia, Cairo, Egypt 2 Department of Mathematics, Basic Education College, Diyala University, Diyala, Iraq Received: • Accepted/Published Online: • Final Version: Abstract: In this paper we introduce some results on difference cordial graphs and describe the difference cordial labeling for some families of graphs. Key words: Difference cordial graph, labeling, families of graphs 1. Introduction In this paper we will deal with finite simple undirected graphs. By G = (V, E) we mean a finite undirected graph with p vertices and q edges where p = |V | and q = |E|. For standard terminology and notations we follow Harary [4], and for more details of labeling see [3]. Ponraj et al. [8] first introduced the concept of difference cordial labeling in 2013 . After that, they introduced many concepts and studied some types of graphs that have this kind of labeling, such as path, cycle, complete graph, complete bipartite graph, bistar, wheel, web, sunflower graph, lotus inside a circle, pyramid, permutation graph, book with n pentagonal pages, t -f old wheel, and double fan, and some more standard graphs were investigated in [6, 7, 8, 9, 10]. Within this area Seoud and Salman introduced some results and investigated some difference cordial graphs: ladder, step ladder, two-sided step ladder, diagonal ladder, triangular ladder, grid graph, and some types of one-point union graphs[11]. Definition [8] Let G = (V, E) be a (p, q) graph, and f be a map from V (G) to {1, 2, ., p} . For each edge uv assign the label |f (v) − f (u)| ; f is called a difference cordial labeling if f is a one-to-one map and |ef (0) − ef (1)| ≤ 1