Discrete Mathematics and Chemistry

Bollobas and Erdos in one of their publications considered the upper bounds on the Randic index [5], which has been known in chemistry as the connectivity index (x) [6]. Undoubtedly, the work Bollobtis and Erdos attracted the interest of many mathematicians in graph theory to the study of the mathematical properties of the Randic index [7,8]. More recently, such woik extended toward the study of several additional topological indices. The Randic index or the connectivity index % is well known in QSAR. It is one of the most often used molecular descriptors in the structure-property-activity studies. As of the middle of 2014, the seminal publication of the connectivity index has passed 2500 citations, in part possibly also due to the continuing interest of mathematicians in the mathematical properties of molecular descriptors. 

The two books on lattice theory that we are recommending have been characterized as Elementary texts recommended for those with limited mathematical maturity It seems therefore appropriate to clarify somewhat ambignons notion of mathematical maturity. What is mathematical matnrity In searching for an answer, we came across a collection of qualities, presented in the list below (most of which we have extracted from [16,17]). On one side, the list below characterizes mathematicians, and on the other side, it allows the rest of us to get an impression of how many mathematical qnalities we may possess We expect many readers may be snrprised to find that they may have several hidden mathematical abilities themselves, which they have not recognized as snch. 

The capacity to generalize from a specific example to broad concept The capacity to handle increasingly abstract ideas To learning throngh nnderstanding 

The capacity to separate the key ideas from the less significant 

The ability to link a geometrical representation with an analytic representation 

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