Integer Cordial and Face Integer Cordial Labeling of Some Flower Graphs

Let G (V, E) be a graph, where V denotes vertex set with |V| = p and E denotes edge set with |E| = q. This paper addresses the labeling of graphs in such a way that the vertices are labeled with an injective mapping g: V → [ − p 2 , … , p 2 ] * or [ └ − p 2 ┘ , … , └ p 2 ┘ ] as p is even or odd respectively which actuate an edge labeling g* such that g*(uv) =1, if g(u) + g(v) > 0 and g* (uv) = 0 if not. The mapping is called an integer cordial labeling if | e g * ( 0 ) − e g * ( 1 ) | ≤ 1, where e g * (j ) signifies the edges labeled with j where j = 0, 1. Based on the integer cordial labeling the faces are labeled with g**: F (G)-→ {0, 1} such that g** (f) = 1 if g**(f) = ∑ j = 1 n g ( v j ) ≥ 0 and g** (f) = 0 if not where Vj are the vertices of f. The mapping is called a face integer cordial labeling if | e g * ( 0 ) − e g * (1) | ≤ 1, where e g * (j ) signifies the edges labeled with j where j = 0, 1 and |f g **(0 ) − f g ** ( 1 ) | ≤ 1 where f g **(j) signifies the faces labeled with j where j = 0, 1 is satisfied.