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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.

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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,

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It appears that the authors don't define a generalized fan graph, but are just using the term "generalized fan graph" to describe these three types of graphs that are the subject of their paper.

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