1. Square with two given adjacent vertices

2. A path is a sequence of distinct adjacent vertices

3. A path is a sequence of distinct adjacent vertices.

4. 3. A strongly regular graph is a regular graph in which every two adjacent vertices have the same number of shared neighbours and every two non-adjacent vertices have the same number of shared neighbours.

5. Every homomorphism of the Petersen graph to itself that doesn't identify adjacent vertices is an automorphism.

6. In other words, it is a four-sided figure in which the line segments between non-adjacent vertices are orthogonal (perpendicular) to each other.

7. Requirement is, that the cyclic order of the adjacent vertices for every vertex of the graph is found out by a topological algorithm for planarity.

8. The Chromatic number of a graph G is the smallest number of colors needed to color the vertices of G so that no two adjacent vertices share the same color (Skiena 1990, p

9. Combinatorially, one can define a polygon as a set of vertices, a set of edges, and an incidence relation (which vertices and edges touch): two adjacent vertices determine an edge, and dually, two adjacent edges determine a vertex.