# Special graphs in graph theory: generalized fan graphs

I was going through some generalized graphs, where I came to know about generalized Petersen and generalized wheel graphs. Details about these two graphs are explained thoroughly on the web and got this link for generalized fan graphs.

I have a little doubt about the generalized fan graphs. Although I know about the fans graphs. Are generalized fan graphs not simple graphs? Can anybody explain the generalized fan graphs. It will be of great help for my work.

The paper you linked to answers your question. No, generalized fan graphs are not necessarily simple. The fan-type graph $$F_{k_1, \dotsc,k_n}$$ denotes the graph that is a path with $$n$$ vertices $$\{v_1,\dotsc,v_n\}$$ in that order, with the addition of a single new vertex $$v_0$$ having $$k_i$$ edges connecting $$v_0$$ to $$v_i$$. Similarly as the paper describes,