A Class Of Diameter Six Trees with Graceful Labeling

Debdas Mishra; Amaresh Chandra Panda; Rajani Ballav Dash

doi:https://doi.org/10.14445/22315373/IJMTT-V9P508

International Journal of Mathematics Trends and Technology

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Volume 9 | Number 1 | Year 2014 | Article Id. IJMTT-V9P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V9P508

A Class Of Diameter Six Trees with Graceful Labeling

Debdas Mishra , Amaresh Chandra Panda , Rajani Ballav Dash

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 we nd diameter four trees consisting of four different combinations of odd, even, and pendant branches with the total number of branches odd. 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, transfers of the rst and second types, BD8TF

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Citation :

Debdas Mishra , Amaresh Chandra Panda , Rajani Ballav Dash, "A Class Of Diameter Six Trees with Graceful Labeling," International Journal of Mathematics Trends and Technology (IJMTT), vol. 9, no. 1, pp. 84-94, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V9P508