Local Antimagic Vertex Coloring of Amalgamation of Path Graph Devi Eka Wardani Meganingtyas*, Ibnu Hadi, Yudi Mahatma, Nadilla Okta Permitasari, Mulyana
State University of Jakarta
*deviekawm[at]unj.ac.id, ibnu_hadi[at]unj.ac.id, Yudi_Mahatma[at]unj.ac.id
Abstract
Graph labeling and coloring is one of the research developments in the field of graphs. The local antimagic labeling on graph G with |V| vertices and |E| edges is defined to be an assignment f: E -> {1,2,...,|E|} so that weights of any two adjacent vertices u and v are distinct. Therefore, any local antimagic labeling induces a proper vertex coloring of G whthe vertex u is assigned the color w(u). The local antimagic chromatic number is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. In this paper, we present the local antimagic chromatic number of path graph operation, especially the type of graph operation is amalgamation.
Keywords: local antimagic coloring, vertex coloring, path, graph operation
