Modification of 2-Connected with Gallai’s Property under 18 Vertices Including Mobius Strip

Abstract

The studies of graph, structure and mathematical molecule have pair-wise relationship among each other is said to be the graph theory. It is important part of discrete mathematics, which is made 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.