10 problems

Let $G=(V,E)$ be a finite simple undirected graph without isolated vertices. A super vertex total local antimagic labeling is a bijection $f:V\cup E\to\{1,2,\dots,|V|+|E|\}$ satisf…

Let $G$ be a finite, simple, undirected graph. A graph is $C$-antimagic if it admits an edge labelling whose vertex sums have at most $C$ conflicts, as defined in the paper. $C$-an…

Let $P_3$ be the path on three vertices. For a graph $H$, a $(1,1)$-antimagic labeling is an antimagic labeling whose vertex sums are exactly $1,2,\ldots,|V(H)|$. Pell-equation exi…

Let $G$ be a graph, let $P_3$ be the path on three vertices, and let $\tau(G)$ be the maximum integer such that the disjoint union of $G$ and $c$ copies of $P_3$ is antimagic for e…

Let $G$ be a regular graph, and let $K_2$ denote the graph with two vertices and one edge. Say that $G$ is antimagic if its edges can be labeled bijectively by $1,2,\ldots,|E(G)|$…

Let $T$ be a tree. An antimagic labeling of $T$ is a bijection $f:E(T)\to\{1,\ldots,|E(T)|\}$ such that the vertex weights … are distinct for every pair of distinct vertices…

Let $G$ be a connected graph. An antimagic labeling of $G$ is a bijection $f:E(G)\to\{1,\ldots,|E(G)|\}$ such that the vertex weights … are distinct for every pair of distinct vert…

Average-degree antimagic conjecture. Every graph with no isolated edges and at most one isolated vertex satisfying this inequality is antimagic; consequently, the least real number…

A graph is vertex-antimagic edge-labelled if its edges receive distinct labels such that the sums of the labels on the edges incident with each vertex are pairwise distinct. Vertex…

Let $G$ be a graph with no isolated edges or vertices, and let its average degree be the average of its vertex degrees. Eccles's conjecture. If the average degree of $G$ is at leas…