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

Keywords

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

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