Group Mean Cordial Labeling of Triangular Snake Related Graphs

Abstract

Let G be a (p, q) graph and let A be a group. Let ???? ∶ ???? (????) → ???? be a map. For each edge xy assign the label⌊ ????(????(????))+????(????(????)) 2 ⌋. Here ????(????(????))denotes the order of ????(????) as an element of the group A. Let I be the set of all integers that are labels of the edges of G. g is called a group mean cordial labeling if the following conditions hold: (1) For a, b ∈ A, |???????? (????) − ???????? (????)| ≤ 1, where ???????? (????) is the number of vertices labeled with a. (2) For r, s ∈ I, |???????? (????) − ???????? (????)| ≤ 1, where ???????? (????) denote the number of edges labeled with r. A graph with a group mean cordial labeling is called a group mean cordial graph. In this paper, we take A as the group of fourth roots of unity and prove that, Triangular snake, Double triangular snake and Alternate triangular snake are group mean cordial graphs.