MODULAR COLORINGS OF CIRCULAR HALIN GRAPHS OF LEVEL TWO
T. NICHOLAS
St. Jude’s College, Thoothoor – 629176, Kanyakumari District, Tamil Nadu, India.
G. R. SANMA *
Department of Mathematics, St. Jude’s College, Kanyakumari District, Tamil Nadu, India.
*Author to whom correspondence should be addressed.
Abstract
For k2, a modular k-coloring of a graph G without isolated vertices is a coloring of the vertices of G with the elements in zk having the property that for every two adjacent vertices of G, the sums of the colors of their neighbours are different in zk.The minimum k for which G has a modular k-coloring is the modular chromatic number of G. In this paper, we determine the modular chromatic number of circular Halin graph.
Keywords: Modular coloring, modular chromatic number, circular Halin graph