INVERSE PROBLEM FOR ALBERTSON IRREGULARITY INDEX
Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, vol.12, no.2, pp.8, 2022 (ESCI)
- Publication Type: Article / Article
- Volume: 12 Issue: 2
- Publication Date: 2022
- Journal Name: Turkish World Mathematical Society Journal of Applied and Engineering Mathematics
- Journal Indexes: Emerging Sources Citation Index (ESCI)
- Page Numbers: pp.8
- Keywords: Inverse problem, Albertson index, irregularity index, topological graph index, GRAPH, TREES
- Open Archive Collection: AVESIS Open Access Collection
- Bursa Uludag University Affiliated: Yes
Abstract
Graph indices have attracted great interest as they give us numerical clues for several properties of molecules. Some indices give valuable information on the molecules under consideration using mathematical calculations only. For these reasons, the calculation and properties of graph indices have been in the center of research. Naturally, the values taken by a graph index is an important problem called the inverse problem. It requires knowledge about the existence of a graph having index equal to a given number. The inverse problem is studied here for Albertson irregularity index as a part of investigation on irregularity indices. A class of graphs is constructed to show that the Albertson index takes all positive even integers. It has been proven that there exists at least one tree with Albertson index equal to every even positive integer but 4. The existence of a unicyclic graph with irregularity index equal to m is shown for every even positive integer m except 4. It is also shown that the Albertson index of a cyclic graph can attain any even positive integer.