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Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

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

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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

On rainbow vertex anti-magic coloring of amalgamation graphs

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pp. 869–881Vol. 28Issue 3April 2025DOI: 10.47974/JDMSC-2137 Crossmark XML
Received:
09 Apr 2024
Published Online:
14 Apr 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2137
Pages:
869–881

Abstract

A rainbow vertex anti-magic coloring represents a relatively new area of exploration in graph theory. This concept extends the idea of rainbow vertex coloring by incorporating elements of anti-magic labeling. Given a function f : E(G)→ {1, 2, …,|E(G)|}, the weight of a vertex v ∈ V(G) under f is given by  wf (v) = Σe∈E(v)  f(e), where E(v) denotes the set of edges incident to v. The function f is classified as a vertex anti-magic edge labeling if the weights assigned to all vertices are distinct. A path is referred to as a rainbow path if for any pair of vertices u and v all internal vertices along the u – v path possess distinct weights. The rainbow vertex anti-magic connection number of G, denoted as rvac(G), is the minimum number of colors required across all rainbow colorings derived from a rainbow vertex anti-magic labeling of G. This paper presents the computation of the rainbow vertex anti-magic connection number for specific graph families, including the Dutch windmill, diamond graph, octopus graph, and amalgamation graph.

Keywords

Rainbow vertex connectionRainbow vertex anti-magic coloringAmalgamation graphs

Subject Classifications

05C78

References

[1] N. Hartsfield and G. Ringel, Pearls in Graph Theory: A Comprehensive Introduction. Courier Corporation (2003).
[2] X. Li and Y. Shi, “On the rainbow vertex-connection,” Discussiones Mathematicae Graph Theory, vol. 33, no. 2, pp. 307-313 (2013).
[3] I. H. Agustin, D. Dafik, and E. Y. Kurniawati, “On Rainbow Vertex Antimagic Coloring of Graphs: A New Notion,” CAUCHY, vol. 7, no. 1, pp. 64-72 (2021).
[4] I. H. Agustin, D. Dafik, E. Y. Kurniawati, and R. Nisviasari, “The rainbow vertex antimagic coloring of tree graphs,” Journal of Physics: Conference Series, vol. 2157, pp. 1-8 (2022).
[5] R. Nisviasari and E. Y. Kurniawati, “On Rainbow Vertex Antimagic Coloring of Shell Related Graphs,” in Proceedings of the 6th International Conference on Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022), vol. 6, p. 17, Springer Nature (Apr. 2023).
[6] I. H. Agustin, D. Dafik, R. Nisviasari, R. I. Baihaki, E. Y. Kurniawati, S. Kartini, and V. Nagaraja, “On Rainbow Vertex Antimagic Coloring and Its Application to the Encryption Keystream Construction,” Appl. Math., vol. 18, no. 4, pp. 783-794 (2024).

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