Iranian Journal of Mathematical Chemistry
Year:2018 | Volume:9 | Issue:3 |Papers Count:7

Design of some crystal and quasicrystal networks, based on rhombellane tiling, is presented. [1, 1, 1]Propellane, is a synthesized organic molecule; its hydrogenated form, the bicyclo[1. 1. 1]pentane, may be represented by the complete bipartite graph K2, 3 which is the smallest rhombellane. Topology of translational and radial structures involving rhombellanes is described in terms of vertex symbol, connectivity sequence, ring sequence and map operations relating structures to their seeds. It is shown, by alternating sum of ranked substructures, that radial structures represent complex constructions of higher rank. Basic properties of rhombellanes, coloring included, are outlined.

Recently, one-two descriptor has been defined and it has been shown that it is a good predictor of the heat capacity at P constant (CP) and of the total surface area (TSA). In this paper, we analyze its generalizations by replacing the value 2 by arbitrary positive value α . We show that these analyses may be on interest, because even good predictions of CP and TSA can be slightly improved. Furthermore, it can be expected that this more general descriptor can find a wider range of application than the original one. The extremal values of trees have been found for all values of α .

Many problems in chemistry, nanotechnology, biology, natural science, chemical physics and engineering are modeled by two point boundary value problems. In general, analytical solution of these problems does not exist. In this paper, we propose a new class of high-order accurate methods for solving special second order nonlinear two point boundary value problems. Local truncation errors of these methods are discussed. To illustrate the potential of the new methods, we apply them for solving some well-known problems, including Troesch’ s problem, Bratu’ s problem and certain singularly perturbed problem. Bratu’ s and Troech’ s problems, may be used to model some chemical reactiondiffusion and heat transfer processes. We also compare the results of this work with some existing results in the literature and show that the new methods are efficient and applicable.

The eccentricity of a vertex v of G is the largest distance between v and any other vertex in G. The reciprocal complementary Wiener (RCW) index of G is defined as..

The "forgotten topological index" or "􀜨 – index" has been introduced by Furtula and Gutman in 2015. The 􀜨 – index of a (molecular) graph is defined as the sum of cubes of the vertex degrees of the graph. In this paper, we compute this topological index for some special graphs such as Wheel graph, Barbell graph and friendship graph. Moreover, the effects on the 􀜨 – index are observed when some operations such as edge switching, edge moving and edge separating are applied to the graphs. Finally, we investigate degeneracy of 􀜨 – index for small graphs.

The reduced reciprocal Randić (RRR) index is a molecular structure descriptor (or more precisely, a topological index), which is useful for predicting the standard enthalpy of formation and normal boiling point of isomeric octanes. In this paper, a mathematical aspect of RRR index is explored, or more specifically, the graph(s) having minimum RRR index is/are identified from the collection of all 􀝊 – vertex connected bicyclic graphs for 􀝊 ≥ 5. As a consequence, the best possible lower bound on the RRR index, for 􀝊 – vertex connected bicyclic graphs is obtained when 􀝊 ≥ 5.