Cordial Labelling Of K-Regular Bipartite Graphs for K = 1, 2, N, N-1 Where K Is Cardinality of Each Bipartition
Pranali Sapre Pranali Sapre · IOSR Journal of Mathematics · 2013
In the labelling of graphs one of the types is cordial labelling.In this we label the vertices 0 or 1 and then every edge will have a label 0 or 1 if the end vertices of the edge have same or different labellings respectively.Here we are going find whether a k-regular bipartite graph can be cordial for different values of k. I.Introduction :If the vertex of G is divided into two subsets A and B such that there is no edge "ab" with B b a or A b a , , then G is said to be bipartite that is, Every edge of G joins a vertex in A to a vertex in B. The sets A and B are called partite sets of G. Complete graph: A graph in which every vertex is adjacent to every other vertex is a complete graph.For a complete graph on n vertices degree of each vertex is n-1. Complete bipartite graph: A bipartite graph G with bipartition ( A,B ) is said to be complete bipartite if every vertex in A is adjacent to every vertex in B and vice versa. Cycle: A closed path is called a cycle. Labelling of a graph:Vertex labelling :It is a mapping from set of vertices to set of natural numbers .Edge labelling :It is a mapping from set of edges to set of natural numbers . Cordial labelling: For a given graph G label the vertices of G "0" or "1".And every edge