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

• Prantik Biswas
• Shahin Shabnam
• Abhisek Paul
• Paritosh Bhattacharya
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 394)

## Abstract

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.

## Keywords

Spanning tree Graph Algorithms Cycle detection Graphic realization Degree sequence Adjacency matrix

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## Authors and Affiliations

• Prantik Biswas
• 1
Email author
• Shahin Shabnam
• 2
• Abhisek Paul
• 1
• Paritosh Bhattacharya
• 1
1. 1.Department of Computer Science and EngineeringNational Institute of TechnologyAgartalaIndia
2. 2.Department of Computer ScienceAssam UniversitySilcharIndia