On Local (a, d)-Edge Antimagic Coloring of Some Specific Classes of Graphs
- 10.2991/978-94-6463-138-8_5How to use a DOI?
- local ( a , d ) $$(a , d)$$ antimagic coloring; edge antimagic coloring; spacial graph
For any graph , the order and size of G are p and q. Let G(V, E) be a graph with the vertex set V and the edge set E, and let w be the edge weight of graph G. with and . A labeling of a graph G is a bijection f from V(G) to the set . The bijection f is called an edge antimagic labeling of graph if for any two vertex u and v in path ,, where , are distinct. Any local edge antimagic labeling induces a proper edge coloring of G where the edge uv is assigned the color w(uv). The local edge antimagic coloring of graph is said to be a local (a, d)-edge antimagic coloring of G if the set of their edge colors form an arithmetic sequence with initial value a and different d. The local (a, d)-edge antimagic chromatic number is the minimum number of colors needed to color G such that a graph G admits the local (a, d)-edge antimagic coloring. Furthermore, In this paper, we will obtain the lower and upper bound of . The results of this research are the exact value of the local (a, d)-edge antimagic chromatic number of some graphs. In this paper we have studied local (a, d)-edge anti-magic coloring on special graphs, namely centipede graphs, lotus graphs, caterpillar graphs, double star graphs, and double broom graphs
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Cite this article
TY - CONF AU - Eric Dwi Putra AU - Dafik AU - Arika Indah Kristiana AU - Robiatul Adawiyah AU - Rafiantika Megahnia Prihandini PY - 2023 DA - 2023/04/27 TI - On Local (a, d)-Edge Antimagic Coloring of Some Specific Classes of Graphs BT - Proceedings of the 6th International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022) PB - Atlantis Press SP - 42 EP - 53 SN - 2352-541X UR - https://doi.org/10.2991/978-94-6463-138-8_5 DO - 10.2991/978-94-6463-138-8_5 ID - Putra2023 ER -