TUTTE POLYNOMIALS OF WHEEL-SUNFLOWER GRAPHS AND THEIR APPLICATIONS

Abstract

We define a graph and call it a wheel-sunflower graph considered as one of the compatibility graphs that may arise in computer-based network information systems. Then we study characterizations that permit us to compute Tutte polynomials of wheel sunflowers using Tutte polynomials of generalized parallel connections. As one of the applications of Tutte polynomials, we characterize wheel-sunflowers by numerical invariants and deduce their T-uniqueness - that is, graphs determined up to isomorphism by their Tutte polynomials. We also apply the theory of Tutte polynomials to determine the component numbers of links corresponding to Wheel-sunflower graphs and show how these numbers change by removing certain edges.