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Odd harmonious labeling of some family of snake graphs.
- Source :
- AIP Conference Proceedings; 11/02/2022, Vol. 2639 Issue 1, p1-7, 7p
- Publication Year :
- 2022
-
Abstract
- Graph labeling is a way of assigning integers to vertices or edges of a graph that satisfy certain conditions. One of graph labeling is odd harmonious labeling. Let G = G(p, q) be a graph that have p vertices and q edges. An odd harmonious labeling of G is an injective function f from the set of vertices of G to the set { 0, 1, 2, ..., 2q - 1} such that the induced function f*, where f*: E(G) → {1, 3, 5, ... , 2q - 1}, and f* (uv) = f(u) + f(v) for every edge uv ∈ E(G), is bijective. A snake graph k(G) is a graph obtained from a path on k edges by replacing each edge by a graph isomorphic to G. If such labeling exists, then G is said to be odd harmonious. In this paper we show that snake graph k(G) is odd harmonious for some graph G. [ABSTRACT FROM AUTHOR]
- Subjects :
- GRAPH labelings
SNAKES
INJECTIVE functions
INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 0094243X
- Volume :
- 2639
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- AIP Conference Proceedings
- Publication Type :
- Conference
- Accession number :
- 159993641
- Full Text :
- https://doi.org/10.1063/5.0111278