In this note we prove with a slight modification of an argument of Cranston et al. [2] that k-regular graphs are antimagic for k ≥ 2.

We present a common generalization of counting lattice points in rational polytopes and the enumeration of proper graph colorings, nowhere-zero flows on graphs, magic squares and graphs, antimagic squares and graphs, compositions of an integer whose parts are partially distinct, and generalized latin squares. Our method is to generalize Ehrhart’s theory of lattice-point counting to a convex pol...

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In this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.

Let m≥1 be an integer and G a graph with m edges. We say that has antimagic orientation if D bijection τ:A(D)→{1,…,m} such no two vertices in have the same vertex-sum under τ, where of vertex v τ is sum labels all arcs entering minus leaving v. Hefetz et al. (2010) conjectured every connected admits orientation. The conjecture was confirmed for certain classes graphs as regular graphs, minimum ...

Consider a simple connected graph $$G = (V,E)$$ of order p and size q. For bijection $$f : E \to \{1,2,\ldots,q\}$$ , let $$f^+(u) \sum_{e\in E(u)} f(e)$$ where $$E(u)$$ is the set edges incident to u. We say f local antimagic labeling G if for any two adjacent vertices u v, we have \ne f^+(v)$$ . The minimum number distinct values $$f^+$$ taken over all denoted by $$\chi_{la}(G)$$ Let $$G[H]$$...