k-Product Cordial Behaviour of Union of Graphs

Abstract

Let f be a map from V (G) to {0, 1, ..., k − 1} where k is an integer, 1 ≤ k ≤ |V (G)|. For each edge uv assign the label f(u)f(v)(mod k). f is called a k-product cordial labeling if |vf (i) − vf (j)| ≤ 1, and |ef (i) − ef (j)| ≤ 1, i, j ∈ {0, 1, ..., k − 1}, where vf (x) and ef (x) denote the number of vertices and edges respectively labeled with x (x = 0, 1, ..., k − 1). In this paper, we investigate the k-product cordial behaviour of union of graphs

k-Product Cordial Labeling of Napier Bridge Graphs

“…In this paper, we find the 3-product and 4-product cordial labeling of Napier bridge graphs P n (3), P n (4) and P n (5). In future, we propose to find the k-product cordial labeling of P n (m) for k ≥ 5 and m ≥ 2.…”

“…In this section, we study the 3-product cordial labeling of Napier bridge graphs P n (3), P n (4) and P n (5).…”

“…The concepts of labeling of graph has gained a lot of popularity in the field of graph theory during the last 60 years due to its wide range of applications. Labeling is a function that 3 we further studied on k-product cordial labeling and established that the following graphs admit/ do not admit k-product cordial labeling: union of graphs [5]; cone and double cone graphs [6]; fan and double fan graphs [7]; powers of paths [8]; the maximum number of edges in a 4-product cordial graph of order p is 4 p−1 4 p− 1 4 + 3 [9]; product of graphs [10] and paths [11]. In this paper, we define a new graph P n (t)…”

“…1, 2, 3. Hence, P n(5) is not a 4-product cordial graph if n ≡ 1(mod 4) forn ≥ Case (iv): If n ≡ 2(mod 4) for n ≥ 14, then |V (P n (5))| = 4t + 2 and |E(P n (5))| = 8t − 2. Thus, v f (i) = t or t + 1 (i = 0, 1, 2, 3) and e f (i) = 2t or 2t − 1 (i = 0, 1, 2, 3).Clearly, v f (0) = t and 0 must be assigned consecutively at the beginning or end of the path.…”