Further Results on Bijective Product k -Cordial Labeling

A bijective product k -cordial labeling f of a graph G with vertex set V and edge set E is a bijection from V to { 1 , 2 , … , | V | } such that the induced edge labeling f × : E ( G ) → Z k = { i | 0 ≤ i ≤ k − 1 } defined as f × ( u v ) ≡ f ( u ) f ( v ) ( mod k ) for every edge u v ∈ E satisfies the condition | e f × ( i ) − e f × ( j ) | ≤ 1 , where i , j ∈ Z k and e f × ( i ) is the number of edges labeled with i under f × . A graph which admits a bijective product k -cordial labeling is called a bijective product k -cordial graph. In this paper, we study bijective product π -cordiality for paths and cycles, where π is an odd prime. We determine bijective product π -cordiality for paths and cycles for 3 ≤ π ≤ 13 . Also, we establish the bijective product k -cordial labeling of stars. Further, we find the bijective product 4-cordial labeling of bistars and the splitting graphs of stars and bistars.