Abstract: We
define the new concept of central graph of a graph G. In this paper we
present results to find the number of edges in the central graphs of cycles and
complete bigraphs and the maximum degree of central graph. We also prove results
relating with the property of connectedness of central graph. We prove a
necessary condition to have an Eulerian central graph and the Hajos union of a
graph and its central graph to be Eulerian. Harmonious colouring on central
graph of and is discussed and we
obtain the harmonious chromatic number of the central graphs of and
.
Keywords and phrases: central graph, harmonious colouring, Hajos union, intersection number, Eulerian.
