Structural Analysis of Quadrilateral Snake Graphs Variants via Reverse Sombor-Based Indices and their Polynomial Formulations
K. M. Saranya
Department of Mathematics, Dr.N.G.P. Arts and Science College, Coimbatore, Tamil Nadu, India.
S. Manimekalai *
Department of Mathematics, Dr.N.G.P. Arts and Science College, Coimbatore, Tamil Nadu, India.
*Author to whom correspondence should be addressed.
Abstract
Topological indices are widely used to describe the structural characteristics of graphs through numerical values. In this work, several variants of quadrilateral snake graphs are analyzed. For these graph classes, reverse degree-based indices including the reverse Sombor index, reverse Elliptic Sombor index, reverse Euler Sombor index, and reverse Harmonic index are computed using edge partition techniques. In addition, the reverse Sombor polynomial is formulated to provide a detailed description of the graph structure. Exlicit expressions are obtained for each class of graphs, and corresponding numerical values are presented to illustrate the results. The outcomes of this work contribute to the ongoing development of topological indices and provide further insight into the strucrtural behavior of quadrilateral snake graph models.
Keywords: Reverse sombor index, reverse Elliptic sombor index, reverse Euler sombor index, reverse harmonic index, reverse sombor polynomial, quadrilateral snake graph, degree-based descriptors