On the Integer-antimagic Spectra of Non-Hamiltonian Graphs

Let $A$ be a nontrivial abelian group. A connected simple graph $G = (V, E)$ is $A$-\textbf{antimagic} if there exists an edge labeling $f: E(G) \to A \setminus \{0\}$ such that the induced vertex labeling $f^+: V(G) \to A$, defined by $f^+(v) = \Sigma$ $\{f(u,v): (u, v) \in E(G) \}$, is a one-to-one map. In this paper, we analyze the group-antimagic property for Cartesian products, hexagonal nets and theta graphs

Group-antimagic Labelings of Multi-cyclic Graphs

Let $A$ be a non-trivial abelian group. A connected simple graph $G = (V, E)$ is $A$-\textbf{antimagic} if there exists an edge labeling $f: E(G) \to A \backslash \{0\}$ such that the induced vertex labeling $f^+: V(G) \to A$, defined by $f^+(v) = \Sigma$ $\{f(u,v): (u, v) \in E(G) \}$, is a one-to-one map. The \textit{integer-antimagic spectrum} of a graph $G$ is the set IAM$(G) = \{k: G \textnormal{ is } \mathbb{Z}_k\textnormal{-antimagic and } k \geq 2\}$. In this paper, we analyze the integer-antimagic spectra for various classes of multi-cyclic graphs

Integer-Magic Spectra of Sun Graphs

國科會研究計畫：NSC 98-2115-M-032-005-MY3[[abstract]]Let N be the set of all positive integers, and Zn={0, 1, 2, …, n-1}. For any h ∈ N, a graph G=(V,E) is said to be Zh-magic if there exists a labeling f : E → Zh\{0} such that induced vertex labeling f+ : V → Zh, defined by f+(v)= ∑uv∈Ef(uv), is a constant map. The integer-magic spectrum of G is the set IM(G)={ h ∈ N|G is Zh-magic}. A sun graph is obtained from attaching a path to each pair of adjacent vertices in an n-cycle. In this paper we showed that the integer-magic spectra of sun graphs are completely determined.[[sponsorship]]國科會[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]CA