Bond Additive Modeling 2. Mathematical Properties of Max-min Rodeg Index

Recently, set of 148 discrete Adriatic indices has been defined. One of these indices is Max-min rodeg index. It is a good predictor of enthalpy of vaporization for octane isomers. It is also good predictor of standard enthalpy of vaporization for octane isomers and it has been shown that it is a good predictor of log water activity coefficient for polychlorobiphenyls. Tight mathematical bounds (expressed as the functions of the number of vertices) are analyzed for the following classes of graphs: connected graphs, trees, unicyclic graphs, chemical graphs, chemical trees, chemical unicyclic graphs and trees with prescribed number of pendant vertices. Further, we analyze maximal value of this index for graphs with maximal degree Δ and minimal value of this index for graphs with minimal degree δ. Also, we propose a series of open problems regarding mathematical properties of discrete Adriatic indices that have shown good predictive properties

Bond Additive Modeling 2. Mathematical Properties of Max-min Rodeg Index

Recently, set of 148 discrete Adriatic indices has been defined. One of these indices is Max-min rodeg index. It is a good predictor of enthalpy of vaporization for octane isomers. It is also good predictor of standard enthalpy of vaporization for octane isomers and it has been shown that it is a good predictor of log water activity coefficient for polychlorobiphenyls. Tight mathematical bounds (expressed as the functions of the number of vertices) are analyzed for the following classes of graphs: connected graphs, trees, unicyclic graphs, chemical graphs, chemical trees, chemical unicyclic graphs and trees with prescribed number of pendant vertices. Further, we analyze maximal value of this index for graphs with maximal degree Δ and minimal value of this index for graphs with minimal degree δ. Also, we propose a series of open problems regarding mathematical properties of discrete Adriatic indices that have shown good predictive properties

Mix-decomposition of the complete graph into directed factors of diameter 2 and undirected factors of diameter 3

We estimate the values, for each k, of the smallest n such that Kn can be mix-decomposed into k undirected factors of diameter 3 and one directed factor of diameter 2. We find the asymptotic value of ratio of n and k, when k tends to infinity and generalize this result for mix-decompositions into p directed factors of diameter 2 and k undirected factors of diameter 3

A graph-theory approach to global determination of octet molecules

Set theory is used to forecast the existence of all possible octet-rule cyclic and acyclic molecules formed from main-group atoms and having ionic and/or covalent bonding with orders up to three

Comparing the Zagreb Indices

Let G = (V, E) be a simple graph with n = |V | vertices and m = |E | edges; let d1, d2, …, dn denote the degrees of the vertices of G. If Δ= maxdi ≤ 4, G is a chemical graph. The first and second Zagreb indices are defined as M1 = Σdi ²and M2 = Σd i d j We show that for all chemical graphs M 1/n ≤ M2/m. This does not hold for all general graphs, connected or not

Bond-additive Modeling. 3. Comparison between the Product-connectivity Index and Sum-connectivity Index

Using the framework of a previously defined procedure (Refs. 16 and 17), we compared the Randic (product-)connectivity index and the sum-connectivity index for the benchmark sets of molecules, that is, 18 octanes, 82 polycyclic aromatic hydrocarbons, 209 polychlorobiphenyls and 22 phenethylamines

Valence connectivity versus Randic, Zagreb and modified Zagreb index: A linear algorithm to check discriminative properties of indices in acyclic molecular graphs

Valence connectivity in molecular graphs is described by 10-tuples mu(ij) where mu(ij) denotes the number of edges connecting vertices of valences i and j. A shorter description is provided by 4-tuples containing the number of vertices and values of Randic, Zagreb and modified Zagreb indices. Surprisingly, these two descriptions are in one-to-one correspondence for all acyclic molecules of practical interest, i.e., for all those having no more than 100 atoms. This result was achieved by developing an efficient algorithm that is linear in the number of 10-tuples

Which Valence Connectivities Realize Monocyclic Molecules: Generating Algorithm and Its Application to Test Discriminative Properties of the Zagreb and Modified Zagreb Indices

Valence connectivities in hydrogen suppressed graphs are characterized by 10-tuples of quantities mij where mij is the number of edges that connect vertices of valences i and j. It is shown which 10-tuples are realizable by monocyclic graphs and this finding is used to compare discriminative properties of the Zagreb and modified Zagreb indices