Critical Hamiltonian Connected Graphs

Abstract

A graph \(G\) is Hamiltonian connected, if there is a Hamiltonian path between every two distinct vertices of \(G\). A Hamiltonian connected graph \(G\) is called critical Hamiltonian connected (CHC), if for every edge \(e\) in \(G\), the graph \(G – e\) is not Hamiltonian connected. In this paper, we study the properties of CHC graphs.