The Basic Parameters Of Four Special Graphs And A Sufficient Condition For Hamiltonian Graphs

In 2018,Nina Zubrilina proved kelenc,Tratnik and Yero’s conjecture on the ratio of edge metric dimension and metric dimension of graphs by using a special kind of graphs.Based on this kind of graphs,we define three kinds of new graphs.We study the properties of these graphs by calculating some parameters of these special graphs and give some concrete examples to understand these four kinds of graphs better.The parameters in this thesis include radius,diameter,detour number,circumference,girth,domination number,independence number,clique number,vertex covering number,edge covering number,decycling number,matching number,chromatic number,vertex-connectivity,integrity and toughness.In studying the related properties of these graphs,we use a sufficient condition for Hamiltonian graphs.There is a gap in the proof given by the authors of the sufficient condition.One case is not considered.We study the case and give a complete proof.