I-Cordial labeling of spider graphs

Abstract

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 V to left perpendicular-p/2..p/2right perpendicular* or[-left perpendicularp/2right perpendicular..left perpendicularp/2right perpendicular] as p is even or odd respectively such that the injective mapping is defined for f (u) f (v) not equal 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 S P (1(m), 2(t)) 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(1(m), 2(t)) and study their characteristics. Here we use the notation left perpendicular-p..pright perpendicular* = left perpendicularp..pright perpendicular - [0] and left perpendicular-p..pright perpendicular = [ x/x is an integer such that vertical bar x vertical bar <= p]