Open AccessSuper total graceful labeling of some trees
Author(s) -
Imroatul Khasanah,
Purwanto Purwanto
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 - 10.1088/1742-6596/1872/1/012004
Subject(s) - combinatorics , bijection , graph labeling , edge graceful labeling , mathematics , graph , simple graph , vertex (graph theory) , bound graph , complement graph , windmill graph , graph power , discrete mathematics , line graph
A graph labeling is an assignment of integers to the edges, vertices, or both of a graph so that it meets to certain conditions. A graph labeling is called total labeling if labeling is given to edges and vertices. Let G be a simple and finite graph having vertex set V(G) , edge set E(G) , number of vertices p , and number of edges q . A super total graceful labeling of G is a bijection f from V(G) ∪ E(G) to the set {1,2,3,…., p + q } such that f(uv) = | f(u) – f(v) | for every uv ∈ E(G) and f(E(G)) = {1,2,3,…, q }. A graph that admits a super total graceful labeling is called a super total graceful graph. In this paper we show that star graph K 1, n , spider graph SP (1 n , 2 m ), and caterpillar graph P 3 ⨀ nK 1 are super total graceful graphs.