Group{1, − 1, i, −i} cordial labeling in some classes of graphs

Cordial labeling is one of a technique that can be applied in error detection and correction in computer coding. Usually graph vertices and edges are labeled with numbers. But a group cordial labeling is the one that labels vertices and edges using elements in a group. A group is a non-empty collection of elements paired with a binary operation satisfying closure, associative, identity and inverse axioms. Order of an element a is the smallest positive integer n such that aⁿ =e, where e is the identity element of the group. An assignment of the elements from the Group{1, − 1, i, −i} to the vertices of a graph in such a way that an edge uv is to have label 1 if labels of the end vertices u, v are relatively prime to each other and label 0 otherwise with an additional condition that number of vertices having with two different labels vary by at most one and total number of edges with labels 0 and 1 vary by at most 1 is alluded as Group {1, − 1, i, −i} cordial labeling. In this paper, we apply the same labeling in the classes of triangular ladder, alternate triangular snake, alternate quadrilateral snake and double triangular snake graphs.