Open AccessThe odd harmonious labelling of nhair-kC 4-snake graph
Author(s) -
Khadija Mumtaz,
Denny Riama Silaban
Publication year - 2021
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 - 10.1088/1742-6596/1725/1/012089
Subject(s) - combinatorics , injective function , graph , mathematics , bijection , complement graph , graph power , discrete mathematics , line graph
Let G ( p , q ) be graph that consists of p = | V | vertices and q = | E | edges, where is the set of vertices and E is the set of edges of G . A graph G ( p , q ) is odd harmonious if there exist an injective function f : V → {0, 1, 2, …, 2 q − 1} that induced a bijective function f ∗ : E → {1, 3, 5, …, 2 q − 1} defined by f ∗ ( uv ) = f ( u ) + f ( v ). The function f is called harmonious labelling of graph G ( p , q ). A hair- kC 4 snake graph is a graph obtain by attaching n leaves to vertices of degree two in kC 4 -snake graph. In this paper we prove that n hair- kC 4 -snake graph is odd harmonious.