A 2-connected graph in two dimensions containing 25 vertices with Gallai's Property

Abstract

Graph theory recently considers as a modern field of mathematics and it was introduced by a great mathematician Leonhard Euler in 1735. Late then it is a flowered in the strong tool used in closely each area of science and nowadays it is most attractive and active area of mathematics research. Actually, graph theory is the study of graph, structure and molecules which have association in each other. It is very essential part of discrete mathematics which has been created with collaboration of nodes (vertices) and edges (lines or links), if a graph is connected with vertices directly by edges it is direct graph or a graph having symmetrically lines is also called direct graph or diagraph. In the studies of graph, we have investigated so many kinds of graph, Hypo-Hamiltonian is one of them. It is most important and it can be defined as the graph which hasn't Hamiltonian cycle but can be developed with the removing of single vertex form the developed graph. Lot of researchers have given the contribution in this research just like Naeem et al has worked on "A Two-Connected Graph with Gallai's Property" containing 12,18 and 25 vertices. In this research paper we have developed two different graphs consisting 25 Eulerian graph which has highest cycle and path order C( G) — 24 and P( G) — 25. Other graph is in 3D under cycle which contains 23 nodes.