Open AccessTotal neighborhood prime labeling of some trees
Author(s) -
T. Jayanth Kumar
Publication year - 2022
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.226
H-Index - 12
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-4819
Subject(s) - combinatorics , mathematics , vertex (graph theory) , edge graceful labeling , prime (order theory) , graph , graph labeling , path graph , degree (music) , discrete mathematics , graph power , physics , line graph , acoustics
Let G be a graph with p vertices and q edges. A total neighborhood prime labeling of G is a labeling in which the vertices and edges are assigned labels from 1 to p + q such that the gcd of labeling in the neighborhood of each non degree 1 vertex is equal to 1 and the gcd of labeling in the edges of each non degree 1 vertex is equal to 1. A graph that admits a total neighborhood prime labeling is called a total neighborhood prime graph. In this paper, we examine total neighborhood prime labeling of trees such as (n, k, m) double star trees, spiders, caterpillars and firecrackers.