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Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

On the local (a, d)-edge antimagic coloring of gear graph and its subdivision

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pp. 883–890Vol. 28Issue 3April 2025DOI: 10.47974/JDMSC-2139 Crossmark XML
Received:
10 Jan 2024
Published Online:
11 Apr 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2139
Pages:
883–890

Abstract

For any graph G = (V, E), with |V(G)| = p and |E(G)|= q. A bijection f : E(G) → {1, 2, 3,...,|E(G)|} is called an local (a,d)-edge antimagic coloring of G if the element of the edge-weight set w(uv) = f(u) + f(v), where w(e1) ≠ w(e2), uv ∈ E(G), are distinct and the set of all edge-weights are formed an arithmetic sequence with initial smallest edge-weight value a and different d. The local (a,d)-edge antimagic chromatic number is is the minimum number of colors needed to color G such that a graph G admits the local (a,d)-edge antimagic coloring.The local (a,d)-edge antimagic chromatic number denoted by χ’(a,d)-ela. In the present, we will obtain the lower and upper bound of χ’(a,d)-ela and determine the exact of value of the local (a,d)-edge antimagic coloring chromatic number of gear graph and it’s subdivisions.

Keywords

Local (ad)-edge antimagic coloring(ad)-edge antimagic coloring chromatic numberGear graph and its subdivision

Subject Classifications

05C1505C78

References

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