- and -labeling problems on interval graphs
For a given graph , the - and -labeling problems assign the labels to the vertices of . Let be the set of non-negative integers. An - and -labeling of a graph is a function such that , for respectively, where represents the distance (minimum number of edges) between the vertices and , and . The - an...
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doaj-18d87db33f7b4ac1b12c29313910dbf92020-11-25T03:37:51ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002017-12-0114320521510.1016/j.akcej.2017.03.00212092624- and -labeling problems on interval graphsSk AmanathullaMadhumangal Pal0Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar UniversityFor a given graph , the - and -labeling problems assign the labels to the vertices of . Let be the set of non-negative integers. An - and -labeling of a graph is a function such that , for respectively, where represents the distance (minimum number of edges) between the vertices and , and . The - and -labeling numbers of a graph , are denoted by and and they are the difference between highest and lowest labels used in - and -labeling respectively. In this paper, for an interval graph , it is shown that and , where represents the maximum degree of the vertices of . Also, two algorithms are designed to label an interval graph by maintaining - and -labeling conditions. The time complexities of both the algorithms are , where represent the number of vertices of .http://dx.doi.org/10.1016/j.akcej.2017.03.002frequency assignment-labeling-labelinginterval graphs |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Sk Amanathulla Madhumangal Pal |
spellingShingle |
Sk Amanathulla Madhumangal Pal - and -labeling problems on interval graphs AKCE International Journal of Graphs and Combinatorics frequency assignment -labeling -labeling interval graphs |
author_facet |
Sk Amanathulla Madhumangal Pal |
author_sort |
Sk Amanathulla |
title |
- and -labeling problems on interval graphs |
title_short |
- and -labeling problems on interval graphs |
title_full |
- and -labeling problems on interval graphs |
title_fullStr |
- and -labeling problems on interval graphs |
title_full_unstemmed |
- and -labeling problems on interval graphs |
title_sort |
- and -labeling problems on interval graphs |
publisher |
Taylor & Francis Group |
series |
AKCE International Journal of Graphs and Combinatorics |
issn |
0972-8600 |
publishDate |
2017-12-01 |
description |
For a given graph , the - and -labeling problems assign the labels to the vertices of . Let be the set of non-negative integers. An - and -labeling of a graph is a function such that , for respectively, where represents the distance (minimum number of edges) between the vertices and , and . The - and -labeling numbers of a graph , are denoted by and and they are the difference between highest and lowest labels used in - and -labeling respectively. In this paper, for an interval graph , it is shown that and , where represents the maximum degree of the vertices of . Also, two algorithms are designed to label an interval graph by maintaining - and -labeling conditions. The time complexities of both the algorithms are , where represent the number of vertices of . |
topic |
frequency assignment -labeling -labeling interval graphs |
url |
http://dx.doi.org/10.1016/j.akcej.2017.03.002 |
work_keys_str_mv |
AT skamanathulla andlabelingproblemsonintervalgraphs AT madhumangalpal andlabelingproblemsonintervalgraphs |
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1724543391898796032 |