Modification in connected graph with satisfying the gallai’s property under eighteen vertices including the novel concept of mobius strip

The studies of graph, structure and mathematical molecule have pair wise relationship among each other is said to be the graph theory. It is an important part of discrete mathematics, which is made up of by vertex called the nodes or points and edges so called links or lines, if the graph has symmetrically lines or links, created as a undirected graph whereas the links joined asymmetrically creates direct graph. There are so many kinds of graph; Hypo-Hamiltonian graph has its own identity it can be defined as a graph if it has not itself a Hamiltonian cycle but each graph developed by eliminating with a single vertex from the graph is Hamiltonian. Naeem Ahmed Kalhoro has worked on "A Two-Connected Graph with Gallai's Property"In his research paper he has applied the property and has found the longest path and cycle in the graph which contains 12 vertices and in the modification of above work we have developed a graph on 18 vertices and have tried to find the longest cycle and path in the proposed graph.