Yazar "Furtula, Boris" seçeneğine göre listele

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    Complementary Topological Indices
    (Univ Kragujevac, Fac Science, 2025) Furtula, Boris; Oz, Mert Sinan
    An edge of a graph can be geometrically represented by points (dr, ds) and (ds, dr) in a 2D coordinate system, where coordinates are, obviously, the degrees of the edge's end-vertices. Recently, using such a geometrical point of view of a graph edge, a couple of topological invariants were put forward. They have attracted considerable attention among chemical graph theorists. This paper introduces a novel approach for devising geometrical topological indices. Finally, special attention is focused on the complementary second Zagreb index as a representative of the introduced approach.
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    Geometric approach to vertex-degree-based topological indices-Elliptic Sombor index, theory and application
    (Wiley, 2024) Gutman, Ivan; Furtula, Boris; Oz, Mert Sinan
    A novel geometric method is proposed for constructing vertex-degree-based molecular structure descriptors (topological indices). The model is based on an ellipse whose focal points represent the degrees of a pair of adjacent vertices. This approach enables a geometric interpretation of several previously known topological indices, and lead to design of a few new. The area of the ellipse induces a vertex-degree-based topological index of remarkable simplicity, which we call elliptic Sombor index(ESO$$ ESO $$). The main mathematical properties of ESO$$ ESO $$ are established, especially its relations to other, earlier known, indices. Then the applicative potential of ESO$$ ESO $$ is analyzed. The elliptic Sombor index (ESO) is a topological molecular descriptor derived from the geometric properties of an ellipse. It is defined by using the equation of the area of an ellipse. image
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    Geometric-Quadratic Index from a Mathematical Perspective
    (Univ Kashan, Fac Mathematical Sciences, 2025) Furtula, Boris; Oz, Mert Sinan
    The geometric-quadratic index (GQ) was defined in 2021 by V. R. Kulli. In a recent study, QSPR analysis for the octane isomers of GQ and some other newly defined topological indices was presented. This analysis has revealed that GQ dominates over many of the well-known topological indices in terms of chemical applicability potential, especially for the heat of vaporization. These results inspired us to investigate the mathematical properties of GQ. In this paper, extremal graphs for GQ are investigated among connected graphs, trees, and unicyclic graphs. In addition, several mathematical relations between GQ and some well-known topological indices are presented. (c) 2025 University of Kashan Press. All rights reserved.
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    On properties of the first inverse Nirmala index
    (Springer, 2025) Furtula, Boris; Oz, Mert Sinan
    The first inverse Nirmala index is a novel degree-based topological descriptor that was introduced in 2021. Preliminary QSPR investigations suggest that this index deserves further consideration because of its unusually good predictive potential. This paper investigates the relations between this index with some elementary graph quantities and some related degree-based topological index. Further, the computational analysis will reveal extremal graphs among trees, molecular trees, all connected graphs, and their molecular counterparts.