This monograph is intended to present the current state of the art of the so-called theory of
geodesic convexity in finite, simple, connected graphs. It has been designed with the …

Treewidth serves as an important parameter that, when bounded, yields tractability for a
wide class of problems. For example, graph problems expressible in Monadic Second Order …

A set S of vertices of a graph G is a geodetic set if every vertex of G lies in a shortest path
between some pair of vertices of S. The Minimum Geodetic Set (MGS) problem is to find a …

We present a new subclass of interval graphs that generalizes connected proper interval
graphs. These graphs are characterized by vertex orderings called connected perfect …

We introduce a new subclass of chordal graphs that generalizes the class of split graphs,
which we call well-partitioned chordal graphs. A connected graph G is a well-partitioned …

In order to model certain social network problems, the strong geodetic problem and its
related invariant, the strong geodetic number, are introduced. The problem is conceptually …

Treewidth is as an important parameter that yields tractability for many problems. For
example, graph problems expressible in Monadic Second Order (MSO) logic and …

We study the complexity of finding the\emph {geodetic number} on subclasses of planar
graphs and chordal graphs. A set $ S $ of vertices of a graph $ G $ is a\emph {geodetic set} …

The strong geodetic problem is a recent variation of the classical geodetic problem. For a
graph G, its strong geodetic number sg (G) sg (G) is the cardinality of a smallest vertex …

Vertex and edge orderings of graphs are commonly used in algorithmic graph theory. Such
orderings can encode structural properties of graphs in a condensed way and, thus, they …