On rainbow antimagic coloring of some graphs
Let G(V, E) be a connected and simple graphs with vertex set V and edge set E. Define a coloring c : E(G) → {1, 2, 3, ..., k}, k ∈ N as the edges of G, where adjacent edges may be colored the same. If there are no two edges of path P are colored the same then a path P is a rainbow path. The graph G...
Saved in:
Published in | Journal of physics. Conference series Vol. 1465; no. 1; pp. 12029 - 12036 |
---|---|
Main Authors | , , , , |
Format | Journal Article |
Language | English |
Published |
Bristol
IOP Publishing
01.02.2020
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | Let G(V, E) be a connected and simple graphs with vertex set V and edge set E. Define a coloring c : E(G) → {1, 2, 3, ..., k}, k ∈ N as the edges of G, where adjacent edges may be colored the same. If there are no two edges of path P are colored the same then a path P is a rainbow path. The graph G is rainbow connected if every two vertices in G has a rainbow path. A graph G is called antimagic if the vertex sum (i.e., sum of the labels assigned to edges incident to a vertex) has a different color. Since the vertex sum induce a coloring of their edges and there always exists a rainbow path between every pair of two vertices, we have a rainbow antimagic coloring. The rainbow antimagic connection number, denoted by rcA(G) is the smallest number of colors that are needed in order to make G rainbow connected under the assignment of vertex sum for every edge. We have found the exact value of the rainbow antimagic connection number of ladder graph, triangular ladder, and diamond. |
---|---|
ISSN: | 1742-6588 1742-6596 |
DOI: | 10.1088/1742-6596/1465/1/012029 |