Geodesic
On a Class of Polynomials Associated with the Stars of a Graph and its Application to Node-Disjoint Decompositions of Complete Graphs and Complete Bipartite Graphs into Stars
Canadian mathematical bulletin, Tome 22 (1979) no. 1, pp. 35-46

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DOI

A star is a connected graph in which every node but possibly one has valency 1. Let G be a graph and C a spanning subgraph of G in which every component is a star. With each component α of C let us associate a weight wα. Let Пα wα be the weight associated with the entire subgraph G the star polynomial of G is ΣПα wα where the summation is taken over all spanning subgraphs of G consisting of stars. In this paper an algorithm for finding star polynomials of graphs is given. The star polynomials of various classes of graphs are then found, and some results about node-disjoint decomposition of complete graphs and complete bipartite graphs are deduced.
DOI : 10.4153/CMB-1979-006-9
Mots-clés : 05C10, 05C99, Graph, star, star polynomial, decomposition of a graph, generating function, node disjoint subgraphs 
Farrell, E. J. On a Class of Polynomials Associated with the Stars of a Graph and its Application to Node-Disjoint Decompositions of Complete Graphs and Complete Bipartite Graphs into Stars. Canadian mathematical bulletin, Tome 22 (1979) no. 1, pp. 35-46. doi: 10.4153/CMB-1979-006-9
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     title = {On a {Class} of {Polynomials} {Associated} with the {Stars} of a {Graph} and its {Application} to {Node-Disjoint} {Decompositions} of {Complete} {Graphs} and {Complete} {Bipartite} {Graphs} into {Stars}},
     journal = {Canadian mathematical bulletin},
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