One special family of graphs is known as circulant graphs.

the vertices of a circulant graph of order labeled with the integers 0,1, −1.

connections between vertices are defined by "jumps" (also given as integers and labeled as that indicate how many vertices to "skip over" when creating edges. a circulant graph is named ;

for example, the circulant graph ; 1,2)has six total vertices (labeled 0, 1, 2, 3, 4, and 5). two vertices are connected if they are 1 step apart (i. e. vertex 0 is connected to vertex 1, vertex 1 is connected to vertex 2, etc.) and vertices are connected if they are two steps apart (i. e. vertex 0 is connected to vertex 2, vertex 1 is connected to vertex 3, connections continue "all the way around the circle."

draw representations of each of the following circulant graphs:

; 2,3) ; 2,4)

; 1,3) ; 2,3,4)

which of the graphs above are connected? note that every circulant graph is regular. can you determine the degree of the vertices in a circulant graph if you are just given the defining "name" of the graph? explain.