Generalized arithmetic staircase graphs and their total edge irregularity strengths
Symmetry, 2022•mdpi.com
Let Γ=(V Γ, E Γ) be a simple undirected graph with finite vertex set V Γ and edge set E Γ. A
total n-labeling α: V Γ∪ E Γ→{1, 2,…, n} is called a total edge irregular labeling on Γ if for
any two different edges xy and x′ y′ in E Γ the numbers α (x)+ α (xy)+ α (y) and α (x′)+ α
(x′ y′)+ α (y′) are distinct. The smallest positive integer n such that Γ can be labeled by a
total edge irregular labeling is called the total edge irregularity strength of the graph Γ. In this
paper, we provide the total edge irregularity strength of some asymmetric graphs and some …
total n-labeling α: V Γ∪ E Γ→{1, 2,…, n} is called a total edge irregular labeling on Γ if for
any two different edges xy and x′ y′ in E Γ the numbers α (x)+ α (xy)+ α (y) and α (x′)+ α
(x′ y′)+ α (y′) are distinct. The smallest positive integer n such that Γ can be labeled by a
total edge irregular labeling is called the total edge irregularity strength of the graph Γ. In this
paper, we provide the total edge irregularity strength of some asymmetric graphs and some …
Let Γ=(VΓ,EΓ) be a simple undirected graph with finite vertex set VΓ and edge set EΓ. A total n-labeling α:VΓ∪EΓ→{1,2,…,n} is called a total edge irregular labeling on Γ if for any two different edges xy and x′y′ in EΓ the numbers α(x)+α(xy)+α(y) and α(x′)+α(x′y′)+α(y′) are distinct. The smallest positive integer n such that Γ can be labeled by a total edge irregular labeling is called the total edge irregularity strength of the graph Γ. In this paper, we provide the total edge irregularity strength of some asymmetric graphs and some symmetric graphs, namely generalized arithmetic staircase graphs and generalized double-staircase graphs, as the generalized forms of some existing staircase graphs. Moreover, we give the construction of the corresponding total edge irregular labelings.
MDPI以上显示的是最相近的搜索结果。 查看全部搜索结果