A Characterization for Ladder like Chemical Structures

Abstract

Molecules are generally symbolized as undirected graphs indicate atoms as nodes and the edges depict covalent bonds between them. The notion of 1-factors is analogous to Kekule structures in chemical graphs. In this article, a new technique based on the covering numbers in graph theory to substantiate the existence of Kekule structures in chemical graphs is proposed. Initially, we study Kekulean graphs which are ladder like, such as crossed prisms, pencil, cubical and cycle of ladder graphs. Using these results, we show that characterizing chemical structures with same vertex and edge covering numbers is beneficial to identify more stable compounds. It is also shown that topped ladders are Kekulean if any one of its node is removed. Furthermore, a necessary and sufficient condition is obtained for graphs in which removal of a node results in a Kekulean graph.