Year: 2025
Type: article
Abstract: Let $$G=(V,E)$$ G = ( V , E ) be a simple graph of size m and L a set of m distinct real numbers. An L - labeling of G is a bijection $$\phi : E \rightarrow L$$ ϕ : E → L . We say that $$\phi $$ ϕ is an antimagic L -labeling if the induced vertex sum $$\phi _+: V \rightarrow {\mathbb {R}}$$ ϕ + : V → R defined as $$\phi _+(u)=\sum _{uv\in E}\phi (uv)$$ ϕ + ( u ) = ∑ u v ∈ E ϕ ( u v ) is injective. Similarly, $$\phi $$ ϕ is a product antimagic L-labeling of G if the induced vertex product $$\phi _{\circ }: V \rightarrow {\mathbb {R}}$$ ϕ ∘ : V → R defined as $$\phi _{\circ }(u)=\prod _{uv\in E}\phi (uv)$$ ϕ ∘ ( u ) = ∏ u v ∈ E ϕ ( u v ) is injective. A graph G is antimagic (resp. product antimagic ) if it has an antimagic (resp. a product antimagic) L -labeling for $$L=\{1,2,\dots ,m\}$$ L = { 1 , 2 , ⋯ , m } . Hartsfield and Ringel conjectured that every simple connected graph distinct from
Authors: Mercè Mora, Joaquín Tey
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4417044091