The reflexive edge strength of toroidal fullerene
AbstractA toroidal fullerene (toroidal polyhex) is a cubic bipartite graph embedded on the torus such that each face is a hexagon. The total k-labeling is defined as a combination of an edge function χe from the edge set to the set [Formula: see text] and a vertex function χv from the vertex set to...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2023-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2022.2150587 |
| Summary: | AbstractA toroidal fullerene (toroidal polyhex) is a cubic bipartite graph embedded on the torus such that each face is a hexagon. The total k-labeling is defined as a combination of an edge function χe from the edge set to the set [Formula: see text] and a vertex function χv from the vertex set to the set [Formula: see text] where [Formula: see text] The total k-labeling of graph Ω such that every two distinctive edges have distinctive weight is called an edge irregular reflexive k-labeling, where for any edge [Formula: see text] the edge weight [Formula: see text] is defined as the summation of the edge label [Formula: see text] itself and its two vertex labels [Formula: see text] and [Formula: see text] The reflexive edge strength of the graph Ω symbolized by, [Formula: see text] is the smallest k for which the graph Ω has an edge irregular reflexive k-labeling. In this paper we determine the exact value of reflexive edge strength of toroidal polyhexes. |
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| ISSN: | 0972-8600 2543-3474 |