Integral sum graphs Gn and G-r,n are perfect graphs
AbstractA graph G is an integral sum graph (sum graph) if its vertices can be labeled with distinct integers (positive integers) so that e = uv is an edge of G if and only if the sum of the labels on vertices u and v is also a label in G. A graph G is perfect if the chromatic number of each of its i...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2023.2251046 |
| _version_ | 1827308450926821376 |
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| author | Julia K. Abraham Sajidha P. Lowell W. Beineke Vilfred V. L. Mary Florida |
| author_facet | Julia K. Abraham Sajidha P. Lowell W. Beineke Vilfred V. L. Mary Florida |
| author_sort | Julia K. Abraham |
| collection | DOAJ |
| description | AbstractA graph G is an integral sum graph (sum graph) if its vertices can be labeled with distinct integers (positive integers) so that e = uv is an edge of G if and only if the sum of the labels on vertices u and v is also a label in G. A graph G is perfect if the chromatic number of each of its induced subgraphs is equal to the clique number of the same. A simple graph G is of class 1 if its edge chromatic number and maximum degree are same. In this paper, we prove that integral sum graphs Gn, [Formula: see text] and [Formula: see text] over the label sets [Formula: see text] and [Formula: see text], respectively, are perfect graphs as well as of class 1 for [Formula: see text]. We also obtain a few structural properties of these graphs. |
| first_indexed | 2024-03-12T02:34:23Z |
| format | Article |
| id | doaj.art-01b3946da54f46799e7bb5707e5fef54 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 2543-3474 |
| language | English |
| last_indexed | 2024-04-24T19:07:56Z |
| publishDate | 2024-01-01 |
| publisher | Taylor & Francis Group |
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| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-01b3946da54f46799e7bb5707e5fef542024-03-26T14:03:25ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742024-01-01211778310.1080/09728600.2023.2251046Integral sum graphs Gn and G-r,n are perfect graphsJulia K. Abraham0Sajidha P.1Lowell W. Beineke2Vilfred V.3L. Mary Florida4Department of Mathematics, Central University of Kerala, Periye, Kerala, IndiaDepartment of Mathematics, Central University of Kerala, Periye, Kerala, IndiaPurdue University, Fort Wayne, IN, USADepartment of Mathematics, Central University of Kerala, Periye, Kerala, IndiaSt. Xavier’s Catholic College of Engineering, Nagercoil, Tamil Nadu, IndiaAbstractA graph G is an integral sum graph (sum graph) if its vertices can be labeled with distinct integers (positive integers) so that e = uv is an edge of G if and only if the sum of the labels on vertices u and v is also a label in G. A graph G is perfect if the chromatic number of each of its induced subgraphs is equal to the clique number of the same. A simple graph G is of class 1 if its edge chromatic number and maximum degree are same. In this paper, we prove that integral sum graphs Gn, [Formula: see text] and [Formula: see text] over the label sets [Formula: see text] and [Formula: see text], respectively, are perfect graphs as well as of class 1 for [Formula: see text]. We also obtain a few structural properties of these graphs.https://www.tandfonline.com/doi/10.1080/09728600.2023.2251046Integral sum graphcovering numberindependence numberchromatic numberclique numberperfect graphs |
| spellingShingle | Julia K. Abraham Sajidha P. Lowell W. Beineke Vilfred V. L. Mary Florida Integral sum graphs Gn and G-r,n are perfect graphs AKCE International Journal of Graphs and Combinatorics Integral sum graph covering number independence number chromatic number clique number perfect graphs |
| title | Integral sum graphs Gn and G-r,n are perfect graphs |
| title_full | Integral sum graphs Gn and G-r,n are perfect graphs |
| title_fullStr | Integral sum graphs Gn and G-r,n are perfect graphs |
| title_full_unstemmed | Integral sum graphs Gn and G-r,n are perfect graphs |
| title_short | Integral sum graphs Gn and G-r,n are perfect graphs |
| title_sort | integral sum graphs gn and g r n are perfect graphs |
| topic | Integral sum graph covering number independence number chromatic number clique number perfect graphs |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2023.2251046 |
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