Some New Classes Of Graceful Diameter Six Trees

Year 2015, Volume: 5 Issue: 2, 269 - 275, 01.12.2015

A. C. Panda D. Mishra

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

Keywords

graceful labeling, diameter six tree, component moving transformation, trans

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