## Some New Classes Of Graceful Diameter Six Trees

## Some New Classes Of Graceful Diameter Six Trees

*A. C. Panda, D. Mishra*

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## 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 pen-dant 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.

## Keywords

Graceful labeling, diameter six tree, component moving transformation, trans-fers of the rst and second types, BD8TF