I-CORDIAL LABELING OF SPIDER GRAPHS

Let G= (V, E) be a graph with p vertices and q edges. A graph G=(V,E)with p vertices and q edges is said to be an I-cordial labeling of a graph if there exists an injective map f from as p is even or odd respectively such 2222 that the injective mapping is defined for f(u) + f(v) ̸= 0 that induces an edge labeling f∗ : E→{0, 1} where f∗(uv) = 1 if f(u) + f(v) > 0 and f∗(uv) = 0 otherwise, such that the number of edges labeled with 1 and the number of edges labeled with 0 differ atmost by 1. If a graph satisfies the condition then graph is called I-Cordial labeling graph or I - Cordial graph. In this paper we intend to prove the spider graph SP(1m,2t) is integer I-cordial labeling graph and obtain some characteristics of I cordial labeling on the graph and we define M-Joins of Spider graph SP(1m,2t) and study their characteristics. Here we use the notation ⌊−p..p⌋∗ = ⌊−p..p⌋ − [0] and ⌊−p..p⌋ = [x/x is an integer such that | x |≤ p]