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On m-Bonacci-Sum Graphs

  • Kalpana MahalingamEmail author
  • Helda Princy RajendranEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11394)

Abstract

We introduce the notion of m-bonacci-sum graphs denoted by \(G_{m,n}\) for positive integers mn. The vertices of \(G_{m,n}\) are \(1,2,\ldots ,n\) and any two vertices are adjacent if and only if their sum is an m-bonacci number. We show that \(G_{m,n}\) is bipartite and for \(n\ge 2^{m-2}\), \(G_{m,n}\) has exactly \((m-1)\) components. We also find the values of n such that \(G_{m,n}\) contains cycles as subgraphs. We also use this graph to partition the set \(\{1,2,\ldots ,n\}\) into \(m-1\) subsets such that each subset is ordered in such a way that sum of any 2 consecutive terms is an m-bonacci number.

Notes

Acknowledgement

The second author wishes to acknowledge the fellowship received from Department of Science and Technology under INSPIRE fellowship (IF170077).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology, ChennaiChennaiIndia

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