A graph $G$ of order $p$ and size $q$ is called an $(a,d)$-edge-antimagic total if there exist a bijection $f : V(G)\cup E(G) \to \{1,2,\dots,p+q\}$ such that the edge-weights, $w(uv)=f(u)+f(v)+f(uv), uv \in E(G)$, ...

For integer $k,r>0,(k,r)$ -coloring of graph $G$ is a proper coloring on the vertices of $G$ by $k$-colors such that every vertex $v$ of degree $d(v)$ is adjacent to vertices with at least $min\{d(v),r\}$ different color. ...

Let $G$ be a simple, connected and undirected graph. Let $r,k$ be natural numbers. By a proper $k$-coloring of a graph $G$, we mean a map $ c : V (G) \rightarrow S$, where $|S| = k$, such that any two adjacent vertices ...