Article ID: MTJPAM-D-25-00152

Title: Extremal Randic type indices


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-25-00152; Volume 7 / Issue 4 / Year 2025, Pages 48-54

Document Type: Research Paper

Author(s): Hacer Ozden Ayna a

aDepartment of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Gorukle 16059 Bursa-Turkey

Received: 10 July 2025, Accepted: 26 February 2026, Published: 21 April 2026

Corresponding Author: Hacer Ozden Ayna (Email address: hozden@uludag.edu.tr)

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Abstract

Vertex degree is one of the most important graph notions and many topological graph indices are degree based including the Randic type graph indices. These indices are calculated in terms of vertex degrees of all the edges in a graph. They have been proven to be very useful in chemical applications. It is an important problem called realizability to find all the graphs corresponding to a given set of non-negative integers as the vertex degrees. Although there are several algorithms about the realizability, there is no complete answer working in all cases. Two recently introduced algorithms called odd and even algorithms are proven already to be very useful for calculating the extremal values of the second Zagreb index. In this work, we apply the same algorithms to determine the extremal values of some Randic type topological graph indices. By knowing the extremal values of such indices, we can eliminate a large workload from the computational studies related to graphs and the modeled chemical and other structures.

Keywords: Randic index, topological graph index, omega invariant, cycle length, odd algorithm, Zagreb index of connected unicyclic graphs

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Cite this article

How to cite this article: H. O. Ayna, Extremal Randic type indices, Montes Taurus J. Pure Appl. Math. 7 (4), 48-54, 2025; Article ID: MTJPAM-D-25-00152.