Add to ORKGA graph is geodetic if each two vertices are joined by a unique shortest path. The problem of characterizing such graphs was posed by Ore in 1962; although the geodetic graphs of diameter two have been described and classified by Stemple and Kantor, little is known of the structure of geodetic graphs in general. In this work, geodetic graphs are studied in the context of convexity in graphs: for a suitable family (PI) of paths in a graph G, an induced subgraph H of G is defined to be (PI)-convex if the vertex-set of H includes all vertices of G lying on paths in (PI) joining two vertices of H. Then G is (PI)-geodetic if each (PI)-convex hull of two vertices is a path. For the family (GAMMA) of geodesics (shortest paths) in G, the (GAMMA)-ge...
Reciprocal version of product degree distance of cactus graphs Let G be a simple graph. A subset S ⊆...
AbstractA graph G is called strongly geodetic if two arbitrary vertices are connected by at most one...
AbstractA graph can be metrized by assigning a length to each of its edges. Such a graph is said to ...
AbstractFor every pair of vertices u,v in a graph, a u-v geodesic is a shortest path from u to v. Fo...
AbstractFor every pair of vertices u,v in a graph, a u–v geodesic is a shortest path from u to v. Fo...
The eccentricity of a vertex vv in a graph GG is the maximum distance of vv from any other vertex of...
AbstractThe usual distance between pairs of vertices in a graph naturally gives rise to the notion o...
AbstractGeneralizing Cook and Pryce's construction procedures for geodetic blocks, an operation in g...
Let G be a graph, u and v two vertices of G, and X a subset of V(G). A u-v geodesic is a path betwee...
The {\em Kneser graph} $K(2n+k,n)$, for positive integers $n$ and $k$, is the graph $G=(V,E)$ such t...
summary:For two vertices $u$ and $v$ of a graph $G$, the closed interval $I[u, v]$ consists of $u$, ...
AbstractA vertex v is a boundary vertex of a connected graph G if there exists a vertex u such that ...
The usual distance between pairs of vertices in a graph naturally gives rise to the notion of an int...
For two vertices u and v of a graph G, the closed interval I[u,v] consists of u, v, and all vertices...
A vertex set S of a graph G is geodetic if every vertex of G lies on a shortest path between two ver...
Reciprocal version of product degree distance of cactus graphs Let G be a simple graph. A subset S ⊆...
AbstractA graph G is called strongly geodetic if two arbitrary vertices are connected by at most one...
AbstractA graph can be metrized by assigning a length to each of its edges. Such a graph is said to ...
AbstractFor every pair of vertices u,v in a graph, a u-v geodesic is a shortest path from u to v. Fo...
AbstractFor every pair of vertices u,v in a graph, a u–v geodesic is a shortest path from u to v. Fo...
The eccentricity of a vertex vv in a graph GG is the maximum distance of vv from any other vertex of...
AbstractThe usual distance between pairs of vertices in a graph naturally gives rise to the notion o...
AbstractGeneralizing Cook and Pryce's construction procedures for geodetic blocks, an operation in g...
Let G be a graph, u and v two vertices of G, and X a subset of V(G). A u-v geodesic is a path betwee...
The {\em Kneser graph} $K(2n+k,n)$, for positive integers $n$ and $k$, is the graph $G=(V,E)$ such t...
summary:For two vertices $u$ and $v$ of a graph $G$, the closed interval $I[u, v]$ consists of $u$, ...
AbstractA vertex v is a boundary vertex of a connected graph G if there exists a vertex u such that ...
The usual distance between pairs of vertices in a graph naturally gives rise to the notion of an int...
For two vertices u and v of a graph G, the closed interval I[u,v] consists of u, v, and all vertices...
A vertex set S of a graph G is geodetic if every vertex of G lies on a shortest path between two ver...
Reciprocal version of product degree distance of cactus graphs Let G be a simple graph. A subset S ⊆...
AbstractA graph G is called strongly geodetic if two arbitrary vertices are connected by at most one...
AbstractA graph can be metrized by assigning a length to each of its edges. Such a graph is said to ...