TY - JOUR

T1 - On the study of rainbow antimagic connection number of comb product of tree and complete bipartite graph

AU - Septory, B. J.

AU - Susilowati, L.

AU - Dafik, D.

AU - Venkatachalam, M.

N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Rainbow antimagic connection number

KW - antimagic labeling

KW - comb product of graphs

KW - rainbow coloring

UR - http://www.scopus.com/inward/record.url?scp=85179484660&partnerID=8YFLogxK

U2 - 10.1142/S1793830923500982

DO - 10.1142/S1793830923500982

M3 - Article

AN - SCOPUS:85179484660

SN - 1793-8309

JO - Discrete Mathematics, Algorithms and Applications

JF - Discrete Mathematics, Algorithms and Applications

M1 - 2350098

ER -