Applications of the Lambert-Tsallis Wq function in graph theory and quantum networks

Abstract

This work brings applications of the Lambert-Tsallis W_q function in graph theory and quantum networks. Initially, the function W_q is used to represent the k colorings of certain classes of chromatic graphs and to describe the positive real root of certain modified orbital polynomials of simple graphs, as well as determining the lower limit for the k colorings of a random graph $G(n,m)$. Subsequently, we will present the disentropy and Renyi-based disentropy, functionals that use the Lambert-Tsallis function in their kernel, of a simple hypergraph in addition to showing the analytical relationship of the Renyi-based disentropy of this hypergraph with its spectral Zeta function. Finally, we will show that the function W_q can be used to quantify the quantum disentanglement of pure two-qubit states in random networks and in probability estimation in some networks with multipartite quantum entanglement percolation and optimal bit-flip correction.