On the Hamiltonicity of Closure of Graph

International Journal of Mathematics Trends and Technology (IJMTT)
© 2021 by IJMTT Journal
Volume-67 Issue-12
Year of Publication : 2021
Authors : Richa Jain


MLA Style: Richa Jain "On the Hamiltonicity of Closure of Graph" International Journal of Mathematics Trends and Technology 67.12 (2021):78-81. 

APA Style: Richa Jain(2021). On the Hamiltonicity of Closure of Graph International Journal of Mathematics Trends and Technology, 67(12), 78-81.

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..


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