Some new graceful generalized classes of diameter six trees

<p>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 o...

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Main Authors: Debdas Mishra, Sushant Kumar Rout, Puma Chandra Nayak
Format: Article
Language:English
Published: Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 2017-04-01
Series:Electronic Journal of Graph Theory and Applications
Subjects:
Online Access:https://www.ejgta.org/index.php/ejgta/article/view/105
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author Debdas Mishra
Sushant Kumar Rout
Puma Chandra Nayak
author_facet Debdas Mishra
Sushant Kumar Rout
Puma Chandra Nayak
author_sort Debdas Mishra
collection DOAJ
description <p>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.</p>
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spelling doaj.art-fd769a30943b464192241a365abb15162022-12-22T03:26:06ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872017-04-01519411110.5614/ejgta.2017.5.1.1081Some new graceful generalized classes of diameter six treesDebdas Mishra0Sushant Kumar Rout1Puma Chandra Nayak2C. V. Raman College of Engineering, Bhubaneswar, IndiaCollege of Engineering and Technology, Bhubaneswar, IndiaBhadrak Autonomous College, Bhadrak, India<p>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.</p>https://www.ejgta.org/index.php/ejgta/article/view/105graceful labeling, diameter six tree, odd and even branches, component moving transformation
spellingShingle Debdas Mishra
Sushant Kumar Rout
Puma Chandra Nayak
Some new graceful generalized classes of diameter six trees
Electronic Journal of Graph Theory and Applications
graceful labeling, diameter six tree, odd and even branches, component moving transformation
title Some new graceful generalized classes of diameter six trees
title_full Some new graceful generalized classes of diameter six trees
title_fullStr Some new graceful generalized classes of diameter six trees
title_full_unstemmed Some new graceful generalized classes of diameter six trees
title_short Some new graceful generalized classes of diameter six trees
title_sort some new graceful generalized classes of diameter six trees
topic graceful labeling, diameter six tree, odd and even branches, component moving transformation
url https://www.ejgta.org/index.php/ejgta/article/view/105
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