A Cycle Detection-Based Efficient Approach for Constructing Spanning Trees Directly from Nonregular Graphic Sequences

Realization of graphic sequences and finding the spanning tree of a graph are two popular problems of combinatorial optimization. A simple graph that realizes a given nonnegative integer sequence is often termed as a realization of the given sequence. In this paper, we have proposed a method for obtaining a spanning tree directly from a degree sequence by applying cycle detection algorithm, provided the degree sequence is graphic and nonregular. The proposed method is a two-step process. First, we apply an algorithm to check whether the input sequence is realizable through the construction of an adjacency matrix corresponding to the degree sequence. Then we apply the cycle detection algorithm separately to generate the spanning tree from it.