The kite graph is the 5-vertex graph illustrated above (Brandstädt et al. 1987, p. 18). It is implemented in the Wolfram
Language as GraphData["KiteGraph"].
Unfortunately, the term is also used to refer to the diamond graph (e.g., West 2000, p. 12) or a tadpole
graph (Kim and Park 2006, Gallian 2018).