In 1956, Nordhaus and Gaddum gave lower and upper bounds on the sum and the product
of the chromatic number of a graph and its complement, in terms of the order of the graph …

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 …

A set S ⊆ V (G) is a hop dominating set of G if for each v ∈ V (G)\S, there exists w ∈ S
such that dG (v, w)= 2. It is a global hop dominating set of G if it is a hop dominating set of …

A geodetic set S of G is said to be a double geo chromatic set Sdg if each u− v geodesic,
where u, v∈ S contains at least two entire color classes of G. The minimum cardinality of a …

This glossary contains an annotated listing of some 300 parameters of graphs, together with
their definitions, and, for most of these, a reference to the authors who introduced them. Let …

A subset S of vertices in a graph G is called a geodetic set if every vertex not in S lies on a
shortest path between two vertices from S. A subset D of vertices in G is called dominating …

In this paper, we study both concepts of geodetic dominating and edge geodetic dominating
sets and derive some tight upper bounds on the edge geodetic and the edge geodetic …

Reciprocal version of product degree distance of cactus graphs Let G be a simple graph. A
subset S? V (G) is a said to be a geodetic set if every vertex u/? S lies on a shortest path …

Let G be an undirected graph with vertex and edge sets V (G) and E (G), respectively. A
subset S of vertices of G is a geodetic hop dominating set if it is both a geodetic and a hop …

Let G be a connected graph. For two vertices u and v in G, a uv geodesic is any shortest path
joining u and v. The closed geodetic interval I_Gu,v consists of all vertices of G lying on any …