Generating spanning tree of non-regular graphic sequences through a variant of Prim´s algorithm

Determining graphic degree sequences and finding the spanning tree of a graph are two popular problems of combinatorial optimization. A simple graph that realizes such a degree sequence is often termed as a realization of the given sequence. In this paper we have proposed a method for generating a spanning tree from a degree sequence, provided the degree sequence is graphic and non-regular. The proposed method first constructs the adjacency matrix corresponding to the degree sequence and then applies a modified version of Prim´s algorithm to generate the spanning tree from it.