Related papers: On $k$-Shifted Antimagic Spider Forests

The concept of antimagic labelings of a graph is to produce distinct vertex sums by labeling edges through consecutive numbers starting from one. A long-standing conjecture is that every connected graph, except a single edge, is antimagic.…

An antimagic labeling of a graph $G(V,E)$ is a bijection $f: E \to \{1,2, \dots, |E|\}$ so that $\sum_{e \in E(u)} f(e) \neq \sum_{e \in E(v)} f(e)$ holds for all $u, v \in V(G)$ with $u \neq v$, where $E(v)$ is the set of edges incident to…

A $k$-antimagic labeling of a graph $G$ is an injection from $E(G)$ to $\{1,2,\dots,|E(G)|+k\}$ such that all vertex sums are pairwise distinct, where the vertex sum at vertex $u$ is the sum of the labels assigned to edges incident to $u$.…

An antimagic labeling for a graph $G$ with $m$ edges is a bijection $f: E(G) \to \{1, 2, \dots, m\}$ so that $\phi_f(u) \neq \phi_f(v)$ holds for any pair of distinct vertices $u, v \in V(G)$, where $\phi_f(x) = \sum_{x \in e} f(e)$. A…

An antimagic labeling of a digraph $D$ with $n$ vertices and $m$ arcs is a bijection from the set of arcs of $D$ to $\{1,2,\cdots,m\}$ such that all $n$ oriented vertex-sums are pairwise distinct, where the oriented vertex-sum of a vertex…

A graph $G=(V,E)$ is strongly antimagic, if there is a bijective mapping $f: E \to \{1,2,\ldots,|E|\}$ such that for any two vertices $u\neq v$, not only $\sum_{e \in E(u)}f(e) \ne \sum_{e\in E(v)}f(e)$ and also $\sum_{e \in E(u)}f(e) <…

An antimagic labeling a connected graph $G$ is a bijection from the set of edges $E(G)$ to $\{1,2,\dots,|E(G)|\}$ such that all vertex sums are pairwise distinct, where the vertex sum at vertex $v$ is the sum of the labels assigned to edges…

A graph $G$ is $k$-$weighted-list-antimagic$ if for any vertex weighting $\omega\colon V(G)\to\mathbb{R}$ and any list assignment $L\colon E(G)\to2^{\mathbb{R}}$ with $|L(e)|\geq |E(G)|+k$ there exists an edge labeling $f$ such that…

An antimagic labelling of a graph is a bijection from the set of edges to $\{1, 2, \ldots , m\}$, such that all vertex-sums are pairwise distinct, where the vertex-sum of a vertex is the sum of labels on the edges incident to it. We say a…

An {\em antimagic labeling} of a graph with $m$ edges and $n$ vertices is a bijection from the set of edges to the integers $1,...,m$ such that all $n$ vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges…

An antimagic labeling of a graph $G$ is a one-to-one correspondence between the edge set $E(G)$ and $\lbrace 1,2,...,|E(G)|\rbrace$ in which the sum of the edge labels incident on the distinct vertices are distinct. Let…

An antimagic labeling of a directed graph $D$ with $m$ arcs is a bijection from the set of arcs of $D$ to $\{1,\dots,m\}$ such that all oriented vertex sums of vertices in $D$ are pairwise distinct, where the oriented vertex sum of a vertex…

An antimagic labelling of a graph $G = (V,E)$ is a bijection from $E$ to $\{1,2, \ldots, |E|\}$, such that all vertex-sums are pairwise distinct, where the vertex-sum of each vertex is the sum of labels over edges incident to this vertex. A…

An antimagic labeling of a graph $G$ is an injection from $E(G)$ to $\{1,2,\dots,|E(G)|\}$ such that all vertex sums are pairwise distinct, where the vertex sum at vertex $u$ is the sum of the labels assigned to edges incident to $u$. A…

An antimagic labeling of a graph $G$ with $m$ edges is a bijection from $E(G)$ to $\{1,2,\ldots,m\}$ such that for all vertices $u$ and $v$, the sum of labels on edges incident to $u$ differs from that for edges incident to $v$. Hartsfield…

A labeling of a graph is a bijection from $E(G)$ to the set $\{1, 2,..., |E(G)|\}$. A labeling is \textit{antimagic} if for any distinct vertices $u$ and $v$, the sum of the labels on edges incident to $u$ is different from the sum of the…

A graph $G$ on $m$ edges is graceful if there is an injection $f : V(G) \to \{0, 1, \ldots, m\}$ whose induced edge labels $\{|f(u) - f(v)| : uv \in E(G)\}$ are exactly $\{1, 2, \ldots, m\}$. Ringel and Kotzig conjectured in 1964 that every…

An antimagic labeling of a directed graph $D$ with $n$ vertices and $m$ arcs is a bijection from the set of arcs of $D$ to the integers $\{1, \cdots, m\}$ such that all $n$ oriented vertex sums are pairwise distinct, where an oriented…

Let $\overrightarrow{G}$ be an oriented graph with the vertex set $V(\overrightarrow{G})$ and the arc set $A(\overrightarrow{G})$. Suppose that $D\subseteq \{0,1,\dots,\partial \}$ is a distance set where $\partial=\max…

Let $m\ge 1$ be an integer and $G$ be a graph with $m$ edges. We say that $G$ has an antimagic orientation if $G$ has an orientation $D$ and a bijection $\tau:A(D)\rightarrow \{1,2,\ldots,m\}$ such that no two vertices in $D$ have the same…