On matching number, decomposition and representation of well-formed graph

In this paper, we find a special type of non-traceable cubic bridge graph called well-formed graph whose central fragment is isomorphic to a hairy cycle and whose branches are pairwise isomorphic. We then show that a well-formed graph can be partition into isomorphic subgraph. Some properties of a well-formed graph such as perfect matching, matching number, decomposition and some parameters for pictorial representation are also provided