SOME NEW CLASSES OF GRACEFUL DIAMETER SIX TREES

Abstract

Here we denote a diameter six tree by (a0; a1, a2,...,am; b1, b2,..., bn; c1, c2,...,cr), where a0 is the center of the tree; ai, i = 1, 2,...,m, bj , j = 1, 2,...,n, and ck, k = 1, 2,...,r are the vertices of the tree adjacent to a0; each ai is the center of a diameter four tree, each bj is the center of a star, and each ck is a pendant vertex. Here we give graceful labelings to some new classes of diameter six trees (a0; a1, a2,...,am; b1, b2,..., bn; c1, c2,...,cr) in which the branches of a diameter four tree incident on a0 are of same type, i.e. either they are all odd branches or even branches. Here by a branch we mean a star, i.e. we call a star an odd branch if its center has an odd degree and an even branch if its center has an even degree.