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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Format: | Article |
Language: | English |
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Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
2017-04-01
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Series: | Electronic Journal of Graph Theory and Applications |
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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> |
first_indexed | 2024-04-12T16:04:53Z |
format | Article |
id | doaj.art-fd769a30943b464192241a365abb1516 |
institution | Directory Open Access Journal |
issn | 2338-2287 |
language | English |
last_indexed | 2024-04-12T16:04:53Z |
publishDate | 2017-04-01 |
publisher | Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia |
record_format | Article |
series | Electronic Journal of Graph Theory and Applications |
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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