Some Types of Zagreb Indices for General Caterpillar Graph and Their Application in Property Predictions of Molecules

Topological indices in graph theory are considered a very important topic because of its practical importance in some branches of sciences, especially in chemistry, physics and networks, because they are closely related to chemical properties and physical properties, including boiling point, melting point, vapor pressure, molar volume etc. There are several types of topological indices, the most important of which are the indices that depend on the degrees of vertices, especially adjacent or non-adjacent vertices. The Zagreb indices for adjacent vertices and non-adjacent vertices, multiplicative and eccentricity for adjacent vertices in a connected simple graph are considered topological indices that have an impact on knowing many chemical and physical properties. In this paper, we discussed the Zagreb type topological indices of generalized caterpillar graphs, as well as for the molecules alkanes with formula CpH(2p + 2), which is a special case of the statement caterpillar graph and studied some of its properties. In the application section, we presented that the first and second Zagreb coindices (corresponding indices) give high correlation among other Zagreb indices when predicting entropy and ascent factor of alkanes.