Inverse problem for sigma index
Date
2018
Authors
Gutman, Ivan
Çevik, Ahmet Sinan
Journal Title
Journal ISSN
Volume Title
Publisher
University of Kragujevac
Abstract
If G is a (molecular) graph and d(v), the degree of its vertex u, then its sigma index is defined as sigma(G) = Sigma(d(u) - d(v))(2), with summation going over all pairs of adjacent vertices. Some basic properties of sigma(G) are established. The inverse problem for topological indices is about the existence of a graph having its index value equal to a given non-negative integer. We study the problem for the sigma index and first show that sigma(G) is an even integer. Then we construct graph classes in which sigma(G) covers all positive even integers. We also study the inverse problem for acyclic, unicyclic, and bicyclic graphs.
Description
Keywords
1st zagreb index, Moleculer-orbitals, Wiener indexes, Graph-theory, Irregularity, Tress
Citation
Gutman, I. vd. (2018). ''Inverse problem for sigma index''. Match, 79(2), 491-508.