On Density of Some Graphs and Their Mycielski Graph

Graph density offers an immediate measure of how tightly a network is connected. This paper gives explicit closed-form formulas for the densities of nine well-known undirected graph, simple, and connected graph families: barbell, friendship, sunlet, banana, lollipop, gear, tadpole, wheel, and fan graphs and their corresponding Mycielski graph. The result supply ready to use expressions that remove the need to build the graphs just to calculate its density. All proofs rely only on counting vertices and edges and substituting them into the definition of density.