(last update: August 22nd 2005)
Thorny Graph Calculator - analyizer of the topological indices, valences and valent bondings
1. Develope an efficient algorithms that will examine existance of monocyclic graph (with prescribed types of thorns) with prescribed one of the following properties:
a) valent bondings
b) Randic index and number of vertices
c) Zagreb index and number of vertices
d) Modified Zagreb index and number of vertices
2) Develope an efficient algorithms that will examine existance of monocyclic graph (with prescribed types of thorns) with prescribed a combination of the following properties:
a) number of vertices of the prescribed valence
b) Zagreb index (for vertices)
c) Modified Zagreb index (for vertices)
d) Randic index (for vertices)
Tipovi trnova koji se promatraju su:
3) Publish achieved scientific results in 2-4 scientific papers.
4) Develope a program in Visual Basic which will solve the problem given by user in less then minute
Connection between chemstry and graph theory is very important. Namely, molecules are ofthen described by graphs, atom correspond to vertices and chemical bonds correpsond to edges. Hence, the application of methods of graph theory is very important in chemistry. We often wander if there exists a molecule with a certain properties. Sometimes, theory of molecular descriptors enables us to reformulate this question into if there exists a molecule with a certain properties. Unfortunately, search for the graph with given properties is not an easy task, because the number of vertices encreases exponentially (with squared exponent) as the number of vertices encreases.
From the grapph theory, it is well known that nonpolynomial algorithm are usually uselless. Hence, it is of great importance to replace such algorithms with polynomial ones. The development of polynomial algorithms is usually based on complex mathematical calculations and here it will be necessary to give an original mathematical results in order to develope the requried algorithms. Based on these theorems the required algorithm (described in project goals) will bw developed.
Darko Veljan, Faculty of Natural Sciences and Education, University of Zagreb, Zagreb, Croatia firstname.lastname@example.org
Zip-file of the program Thorny Graph Calculator can be downloaded here.
Maunuals of the program Thorny Graph Calculator can be downloaded here.
Technical details of the paper Thorny graphs I. Valence connectivities, MATCH, in pdf-format can be downloaded here.