A STUDY ON ODD EVEN CONGRUENCE LABELLING OF DIGRAPH

Abstract: This paper investigates the existence of odd-even congruence labelling for various classes of graphs, including a splitting graph of bistars, corona products, tensor products shadow graphs and tadpole graph. A graph G(V,E) is defined as an odd-even congruence graph if there exists a bijective mapping f:V(G)→{1,3,5,……,2|V|-1} and an injective mapping f^*:E(G)→{2,4,6,……,2|E|} such that for every edge uv∈E(G), the condition f^* (uv)| |f(u)-f(v) is satisfied. In addition, constructive proofs and labelling algorithms to demonstrate that these specific graph structures, arising from products and splitting operations, admit such a labelling scheme are provided.

Keywords: Graph labelling, odd-even congruence, splitting graph of bistar graph, corona product, tensor product, tadpole graph and shadow graph.