When fieldwork takes a detour.

Detour Monophonic Graphoidal Covering Number of Corona Product Graph of Some Standard Graphs with the Wheel

A chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path  $P$ is called a monophonic path if it is a chordless path. A longest $x-y$ monophonic path is called an $x-y$ detour monophonic path. A  detour monophonic graphoidal cover of a graph $G$ is a collection $psi_{dm}$ of detour monophonic paths in $G$ such that every vertex of $G$ is an internal vertex  of at most on...

The explicit relation among the edge versions of detour index

The vertex version of detour index was defined during the works on connected graph in chemistry. The edge versions of detour index have been introduced ecently. In this paper, the explicit relations among edge versions of detour index have been declared and due to these relations, we compute the edge detour indices for some well-known graphs.

The tree longest detour problem in a biconnected graph

In a biconnected graph, a detour is the best alternative path from a detour-starting vertex to the destination vertex. A detour-starting vertex is the vertex from which the original shortest path is changed. The longest detour (LD) problem is to find a detour-critical edge in a shortest path such that the removal of the edge results in the maximum distance increment. In this paper, we deal with...

The latitudinal herbivory-defence hypothesis takes a detour on the map.

On edge detour graphs

For two vertices u and v in a graph G = (V, E), the detour distance D(u, v) is the length of a longest u–v path in G. A u–v path of length D(u, v) is called a u–v detour. A set S ⊆ V is called an edge detour set if every edge in G lies on a detour joining a pair of vertices of S. The edge detour number dn1(G) of G is the minimum order of its edge detour sets and any edge detour set of order dn1...