A note on the Independence Polynomial of 3-Regular 2-Connected Planar Graphs Maximizing Triangular Elements

	A note on the Independence Polynomial of 3-Regular 2-Connected Planar Graphs Maximizing Triangular Elements
Communications in Combinatorics and Optimization
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 مهر 1405
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2026.30571.2538
نویسندگان
Nakshee Mehta؛ S. Veeramani^*
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore - 632 014, Tamil Nadu, India
چکیده
We establish a sharp upper bound on the number of triangles in 3-regular planar graphs. To demonstrate the tightness of this bound, we construct a finite family of 3-regular, 2-connected planar graphs that attain it, and we provide a complete characterization of the resulting extremal structures. Building on this characterization, we derive closed-form expressions for the independence polynomials of these extremal graphs. Together, these results establish an explicit connection between extremal tri- angle configurations in 3-regular planar graphs and the algebraic structure encoded in their independence polynomials, offering new insight into how local combinatorial extremality is reflected in global algebraic invariants.
کلیدواژه‌ها
Regular graphs؛ Graph indices؛ Planar graphs؛ Independence polynomial؛ connectivity

آمار تعداد مشاهده مقاله: 13

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