Abstract
Let G be a simple connected graph. An i-subset of V(G) is a subset of V(G) of cardinality i. An induced i-star of G is a star in G induced by an i-subset of V(G). The star polynomial representation of G is the generating function of the sequence of the number of induced i-stars in G. In this paper, we establish the star polynomials of some special graphs such as the star graph, spider graph, complete bipartite graph, and the complete q-partite graph.
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