On Local Antimagic Chromatic Number of Cycle-Related Join Graphs
An edge labeling of a connected graph = ( , ) is said to be local antimagic if it is a bijection : → {1, . . ., | |} such that for any pair of adjacent vertices and , ) ≠ ), where the induced vertex label ) = Σ ), with ranging over all the edges incident to . The local antimagic chromatic number of...
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| Veröffentlicht in: | Discussiones Mathematicae. Graph Theory 2021-02, Vol.41 (1), p.133-152 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | An edge labeling of a connected graph
= (
,
) is said to be local antimagic if it is a bijection
:
→ {1, . . ., |
|} such that for any pair of adjacent vertices
and
,
) ≠
), where the induced vertex label
) = Σ
), with
ranging over all the edges incident to
. The local antimagic chromatic number of
, denoted by
), is the minimum number of distinct induced vertex labels over all local antimagic labelings of
. In this paper, several sufficient conditions for
) ≤
) are obtained, where
is obtained from
with a certain edge deleted or added. We then determined the exact value of the local antimagic chromatic number of many cycle-related join graphs. |
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| ISSN: | 1234-3099 2083-5892 |
| DOI: | 10.7151/dmgt.2177 |