On the zero ring index of some classes of graphs

• Main Authors: Maniago, Adrian A., Yusoph, Feeroz R.
• Format: text
• Language: English
• Published: Animo Repository 2018
• Subjects: Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/18569
• Institution: De La Salle University

This study focuses on a labeling of the vertices of a graph G. A zero ring is a ring denoted by R0 where the product of any two distinct elements is equal to 0, the additive identity of the ring. A zero ring labeling of G is an assignment f of elements of R0 to the vertices of G such that f(x) + f(y) 6= 0 whenever x y are adjacent in G. It is known that every graph has a zero ring labeling, so an interesting problem to consider is to determine the smallest positive integer (G) such that there exists a zero ring R0 of order (G) for which G admits a zero ring labeling. This graph parameter is called the zero ring index of the graph G. In this paper, we aim to discuss the zero ring indices of some common classes of graphs, such as paths, fans, wheels, helms, complete bipartite graphs, complete tripartite graphs, and complete four-partite graphs. Furthermore, we aim to determine the zero ring index of a general multi-partite graph, and to discuss characterizations for graphs whose zero ring indices are equal to their order.