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Sushant Kumar Rout
College of Engineering and Technology, Bhubaneswar, India
Electrical & Electronics Engineering

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Some new graceful generalized classes of diameter six trees Debdas Mishra; Sushant Kumar Rout; Puma Chandra Nayak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 1 (2017): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2017.5.1.10

Abstract

Here we denote a {\it diameter six tree} by $(c; a_{1}, a_{2}, \ldots, a_{m};   b_{1}, b_{2}, \ldots,  b_{n}; c_{1}, c_{2}, \ldots, c_{r})$, where $c$ is the center of the tree; $a_{i}, i = 1, 2, \ldots, m$, $b_{j},  j =  1, 2, \ldots, n$, and $c_{k}, k = 1, 2, \ldots, r$ are the vertices of the tree adjacent to $c$; each $a_{i}$  is the center of a diameter four tree, each $b_{j}$ is the center of a star, and each $c_{k}$ is a pendant vertex. Here we give graceful labelings to some new classes of diameter six trees $(c;  a_{1}, a_{2}, \ldots, a_{m};  b_{1}, b_{2}, \ldots, b_{n}; c_{1}, c_{2}, \ldots, c_{r})$ in which a diameter four tree may contain any combination of branches with the total number of branches odd though with some conditions on the number of odd, even, and pendant 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, an even branch if  its center has an even degree, and a pendant branch if it is a pendant vertex.
Co-Authors Debdas Mishra Puma Chandra Nayak