Draw the graph whose vertex set is the set of integers from 1 to 7, and two vertices x and y are adjacent if $|x − y| ≡ 0(mod 2)$.

Question

So i was given this question

Draw the graph whose vertex set is the set of integers from 1 to 7, and two vertices x and y are adjacent if $|x − y| ≡ 0(mod 2)$. Is the graph simple, count the degree of each vertex, By adding some edges is it possible to transform it into Eulerian one?

What is really throwing me off is the $|x − y| ≡ 0(mod 2)$ part.

In a simple graph the edges form a set and each edge is a unordered pair of distinct vertices. In a simple graph with n vertices, the degree of every vertex is at most n − 1. So since the graph would be adjacent to $|x − y| ≡ 0(mod 2)$ it would be simple because it can evenly divide.

Answer 1

The graph is the union of two complete subgraphs: $1,3,5,7$ and $2,4,6$. Note: each vertex also has a loop.