We study edge-sum distinguishing labeling, a type of labeling recently introduced by Z. Tuza (2017) in context games. An ESD an $n$-vertex graph $G$ is injective mapping integers $1$ to $l$ its vertices such that for every edge, the sum on endpoints unique. If $ l$ equals $n$, we speak about canonical labeling. focus primarily structural properties this and show several classes graphs if they h...

The paper deals with the problem of labeling the vertices and edges of a plane graph in such a way that the labels of the vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called d-antimagic if for every positive integer s, the s-sided face weights form an arithmetic progression with a difference d. Such a labeling is called super if the sm...

Let G = (V (G), E(G), F (G)) be a simple, finite, connected, plane graph with the vertex set V (G), the edge set E(G) and the face set F (G). A labeling of type (1, 1, 1) assigns labels from the set {1, 2, . . . , |V (G)|+ |E(G)| + |F (G)|} to the vertices, edges and faces of a plane graph G, such that each vertex, edge and face receives exactly one label and each number is used exactly once as...

Let \(G=(V, E)\) be a simple graph and \(H\) subgraph of \(G\). Then \(G\) admits an \(H\)-covering, if every edge in \(E(G)\) belongs to at least one that is isomorphic \(H\). An \((a,d)-H\)-antimagic total labeling bijection \(f:V(G)\cup E(G)\rightarrow \{1, 2, 3,\dots, |V(G)| + |E(G)|\}\) such for all subgraphs \(H'\) \(H\), the weights \(w(H') =\sum_{v\in V(H')} f (v) \sum_{e\in E(H')} (e)\...

The study of valuations of graphs is a relatively young part of graph theory. In this article we survey what is known about certain graph valuations, that is, labeling methods: antimagic labelings, edge-magic total labelings and vertex-magic total labelings.