On the study of rainbow antimagic connection number of comb product of tree and complete bipartite graph

B. J. Septory, L. Susilowati, D. Dafik, M. Venkatachalam

Research output: Contribution to journalArticlepeer-review

Abstract

Rainbow antimagic coloring is the combination of antimagic labeling and rainbow coloring. The smallest number of colors induced from all edge weights of antimagic labeling is the rainbow antimagic connection number of G, denoted by &rac(G). Given a graph G with vertex set V (G) and edge set E(G), the function f from V (G) to 1, 2,⋯,V (G)} is a bijective function. The associated weight of an edge yz E(G) under f is w(yz) = f(y) + f(z). A path R in the vertex-labeled graph G is said to be a rainbow y - z path if for any two edges yz,y'z' E(R) it satisfies w(yz) w(y'z'). The function &f is called a rainbow antimagic labeling of G if there exists a rainbow y - z path for every two vertices y,z V (G). When we assign each edge yz with the color of the edge weight w(yz), we say the graph G admits a rainbow antimagic coloring. In this paper, we show the new lower bound and exact value of the rainbow antimagic connection number of comb product of any tree and complete bipartite graph.

Original languageEnglish
Article number2350098
JournalDiscrete Mathematics, Algorithms and Applications
DOIs
Publication statusAccepted/In press - 2023

Keywords

  • Rainbow antimagic connection number
  • antimagic labeling
  • comb product of graphs
  • rainbow coloring

Fingerprint

Dive into the research topics of 'On the study of rainbow antimagic connection number of comb product of tree and complete bipartite graph'. Together they form a unique fingerprint.

Cite this