On the Hamiltonicity of Closure of Graph

Richa Jain

doi:https://doi.org/10.14445/22315373/IJMTT-V67I12P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 12 | Year 2021 | Article Id. IJMTT-V67I12P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I12P509

On the Hamiltonicity of Closure of Graph

Richa Jain

Abstract

In this paper we discuss about the number of spanning cycles in closure of graph. The closure of a graph G is the graph obtained by adding edges between non-adjacent vertices whose degree sum is at least |V(G)|, until this can no longer be done. There are countless generalizations of paths and cycles and Hamiltonian properties in graphs, and one of these generalizations is the uniquely Hamiltonian graph. A graph is uniquely Hamiltonian if it contains exactly one spanning cycle. We proved the results about the Hamiltonicity, uniquely Hamiltonicity of closure of graph.

Keywords

Line graph, length of path, spanning cycle, spanning path, etc.

References

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Citation :

Richa Jain, "On the Hamiltonicity of Closure of Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 12, pp. 78-81, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I12P509