Open AccessCertain Results on Prime and Prime Distance Labeling of Graphs
Author(s) -
A. Parthiban,
Ajaz Ahmad Pir,
A. Felix
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1531/1/012062
Subject(s) - combinatorics , mathematics , bijection , edge graceful labeling , graph , prime (order theory) , graph labeling , injective function , discrete mathematics , prime number , graph power , line graph
Let G be a graph on n vertices. A bijective function f : V ( G ) → {1, 2,…, n } is said to be a prime labeling if for every e = xy , GCD{ f ( x ), f ( y )} = 1. A graph which permits a prime labeling is a “prime graph”. On the other hand, a graph G is a prime distance graph if there is an injective function g : V ( G ) → Z (the set of all integers) so that for any two vertices s & t which are adjacent, the integer | g ( s ) – g ( t )| is a prime number and g is called a prime distance labeling of G . A graph G is a prime distance graph (PDL) iff there exists a “prime distance labeling” (PDL) of G . In this paper, we obtain the prime labeling and prime distance labeling of certain classes of graphs.