INVERSE PROBLEM FOR ALBERTSON IRREGULARITY INDEX

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 b...

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Bibliographic Details
Published in:TWMS journal of applied and engineering mathematics 2022-07, Vol.12 (3), p.808
Main Authors: Gunes, A.Y, Togan, M, Demirci, M, Cangul, I.N
Format: Article
Language:English
Subjects:
Integers
Inverse problems
Irregularities
Mathematical analysis
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Summary: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. Keywords: Inverse problem, Albertson index, irregularity index, topological graph index. AMS Subject Classification: 05C07, 05C10, 05C30.
ISSN:2146-1147
2146-1147