The paw graph is the 3-pan graph, which is also isomorphic to the 
-tadpole
graph.
It is implemented in the Wolfram Language as GraphData["PawGraph"].
Paw Graph
See also
Lollipop Graph, Pan Graph, Tadpole GraphExplore with Wolfram|Alpha
References
Brandstädt, A.; Le, V. B.; and Spinrad, J. P. Graph Classes: A Survey. Philadelphia, PA: SIAM, p. 18, 1987.ISGCI: Information System on Graph Class Inclusions v2.0. "List of Small Graphs." http://www.graphclasses.org/smallgraphs.html.West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 12, 2000.Cite this as:
Weisstein, Eric W. "Paw Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PawGraph.html