## What is detour distance?

## What is detour distance?

The detour distance between vertices and of a graph is the length of a longest path between. them, denoted by. In this paper we introduce Detour maximum distance of a graph denoted by. by considering the sum of the degrees of vertices presented in the path, the length of the longest path in addition.

## Is the Petersen graph 3 colorable?

The Petersen graph has chromatic number 3, meaning that its vertices can be colored with three colors — but not with two — such that no edge connects vertices of the same color. It has a list coloring with 3 colors, by Brooks’ theorem for list colorings.

**What is the distance in graph theory?**

In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path distance.

### Is Petersen graph homeomorphic to K5?

2. Prove that the Petersen graph (shown below) is not planar by finding a subgraph that is homeomorphic to K3,3 or K5. It is impossible to find a subgraph homeomorphic to K5 since we would require a vertex of degree 4.

### Is Herschel graph Hamiltonian?

In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges, the smallest non-Hamiltonian polyhedral graph. It is named after British astronomer Alexander Stewart Herschel.

**What is the difference between Euclidean distance and geodesic distance?**

The Geodesic distance is the distance of the minimum length inside the figure path and the Euclidean distance is the straight line distance.

#### Why is the Petersen graph not Hamiltonian?

The Petersen graph has no Hamiltonian cycles, but has a Hamiltonian path between any two non-adjacent vertices. In fact, for sufficiently large vertex sets, there is always a graph which admits a Hamiltonian path starting at every vertex, but is not Hamiltonian.

#### How many edges are in K5?

10 edges

K5: K5 has 5 vertices and 10 edges, and thus by Lemma 2 it is not planar. K3,3: K3,3 has 6 vertices and 9 edges, and so we cannot apply Lemma 2.

**Who invented Hamiltonian path?**

A directed graph in which the path begins and ends on the same vertex (a closed loop) such that each vertex is visited exactly once is known as a Hamiltonian circuit. The 19th-century Irish mathematician William Rowan Hamilton began the systematic mathematical study of such graphs.