Local total anti-magic chromatic number of graphs
Let G=(V,E) be a graph without isolated vertices and let |V(G)|=n and |E(G)|=m. A bijection π:V(G)∪E(G)→{1,2,....,n+m} is said to be local total anti-magic labeling of a graph G if it satisfies the conditions: (i.) for any edge uv, ω(u)≠ω(v), where u and v in V(G) (ii.) for any two adjacent edges e...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-07-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844023049691 |
| _version_ | 1797771517266755584 |
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| author | V. Sandhiya M. Nalliah |
| author_facet | V. Sandhiya M. Nalliah |
| author_sort | V. Sandhiya |
| collection | DOAJ |
| description | Let G=(V,E) be a graph without isolated vertices and let |V(G)|=n and |E(G)|=m. A bijection π:V(G)∪E(G)→{1,2,....,n+m} is said to be local total anti-magic labeling of a graph G if it satisfies the conditions: (i.) for any edge uv, ω(u)≠ω(v), where u and v in V(G) (ii.) for any two adjacent edges e and e′, ω(e)≠ω(e′) (iii.) for any edge uv∈E(G) is incident to the vertex v, ω(v)≠ω(uv), where weight of vertex u is, ω(u)=∑e∈S(u)π(e), S(u) is the set of edges with every edge of S(u) one end vertex is u and an edge weight is ω(e=uv)=π(u)+π(v). In this paper, we have introduced a local total anti-magic labeling (LTAL) and the local total anti-magic chromatic number (LTACN). Also, we obtain the LTACN for the graphs Pn, K1,n, Fn and Sn,n. |
| first_indexed | 2024-03-12T21:38:43Z |
| format | Article |
| id | doaj.art-b05d7836163a4f79b166d95f7ad4e2d5 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-03-12T21:38:43Z |
| publishDate | 2023-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-b05d7836163a4f79b166d95f7ad4e2d52023-07-27T05:57:21ZengElsevierHeliyon2405-84402023-07-0197e17761Local total anti-magic chromatic number of graphsV. Sandhiya0M. Nalliah1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, IndiaCorresponding author.; Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, IndiaLet G=(V,E) be a graph without isolated vertices and let |V(G)|=n and |E(G)|=m. A bijection π:V(G)∪E(G)→{1,2,....,n+m} is said to be local total anti-magic labeling of a graph G if it satisfies the conditions: (i.) for any edge uv, ω(u)≠ω(v), where u and v in V(G) (ii.) for any two adjacent edges e and e′, ω(e)≠ω(e′) (iii.) for any edge uv∈E(G) is incident to the vertex v, ω(v)≠ω(uv), where weight of vertex u is, ω(u)=∑e∈S(u)π(e), S(u) is the set of edges with every edge of S(u) one end vertex is u and an edge weight is ω(e=uv)=π(u)+π(v). In this paper, we have introduced a local total anti-magic labeling (LTAL) and the local total anti-magic chromatic number (LTACN). Also, we obtain the LTACN for the graphs Pn, K1,n, Fn and Sn,n.http://www.sciencedirect.com/science/article/pii/S2405844023049691Local anti-magic graphsChromatic numberVertex weightEdge weight |
| spellingShingle | V. Sandhiya M. Nalliah Local total anti-magic chromatic number of graphs Heliyon Local anti-magic graphs Chromatic number Vertex weight Edge weight |
| title | Local total anti-magic chromatic number of graphs |
| title_full | Local total anti-magic chromatic number of graphs |
| title_fullStr | Local total anti-magic chromatic number of graphs |
| title_full_unstemmed | Local total anti-magic chromatic number of graphs |
| title_short | Local total anti-magic chromatic number of graphs |
| title_sort | local total anti magic chromatic number of graphs |
| topic | Local anti-magic graphs Chromatic number Vertex weight Edge weight |
| url | http://www.sciencedirect.com/science/article/pii/S2405844023049691 |
| work_keys_str_mv | AT vsandhiya localtotalantimagicchromaticnumberofgraphs AT mnalliah localtotalantimagicchromaticnumberofgraphs |