Chromatic symmetric functions and combinatorial polynomials are central constructs in modern algebraic combinatorics, extending classical graph invariants into rich algebraic frameworks. Originating ...

Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

The second path matrix S(G) collects all the second paths in the graph G. Its characteristic polynomial shows some regularity in several particular graphs, such as paths, cycles, stars and complete ...

Python allows free creation of plots, unlike expensive, stagnant graphing calculators. Import NumPy and Matplotlib for basic linear and polynomial plots in Python. Seaborn lets you make statistical ...

Vol. 31, No. 1, The 23rd International Conference on Finite and Infinite Dimensional Complex Analysis and Applications (2017), pp. 9-16 (8 pages) Abstract.The aim of this paper is to investigate and ...

Computer scientists are abuzz over a fast new algorithm for solving one of the central problems in the field. (January 15, 2017, update: On January 4, Babai retracted his claim that the new algorithm ...

Illustration of a set of real zeros of a graph polynomial (middle) and two Feynman diagrams. Credit: Max Planck Institute for Mathematics in the Sciences How can the behavior of elementary particles ...

For non-planar graphs, such solutions are computationally intractable," explained the researchers. The algorithm relies on the Kac-Ward formalism, a mathematical method that allows exact computation ...