Many real transportation and mobility networks have their vertices placed on the surface of the Earth. In such embeddings, the edges laid on that surface may cross. In his pioneering research, Moon analyzed the distribution ...

A partition ¿ ={S1,...,Sk}of the vertex set of a connected graphGis called aresolvingpartitionofGif for every pair of verticesuandv,d(u,Sj)6=d(v,Sj), for some partSj. Thepartition dimensionßp(G) is the minimum cardinality ...

Let u;v be two vertices of a connected graph G . The vertex v is said to be a boundary vertex of u if no neighbor of v is further away from u than v . The boundary of a graph is the set of all its ...

A k-coloring of a graph G is a partition of the vertices of G into k independent sets, which are called colors. A k-coloring is neighbor-locating if any two vertices belonging to the same color can be distinguished from ...

In the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to ...

Ak-coloringof a graphGis a partition of the vertices ofGintokindependent sets,which are calledcolors. Ak-coloring isneighbor-locatingif any two vertices belongingto the same color can be distinguished from each other by ...

A total dominating set of a graph is a subset of such that every vertex in is adjacent to at least one vertex in . The total domination number of , denoted by , is the minimum cardinality of a total dominating set of . A ...

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

Many problems related to location and domination give raise to different parameters in graphs. The aim is to determine the location of some facility, object, item by placing watchers in some vertices of the graph. Watching ...