Abstract: Recent work by Marcus, Spielman and Srivastava proves the existence of bipartite Ramanujan (multi) graphs of all degrees and all sizes. However, that paper did not provide a polynomial time ...

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This is the first book to comprehensively cover chromatic polynomials of graphs. It includes most of the known results and unsolved problems in the area of chromatic polynomials. Dividing the book ...

A simple application made to visualise a polynomial function for a possibly having a maximum power of three. Any lower down to y = 0 will work as well. This is a project made for the university I am ...

Department of Mathematics and Statistics, Qinghai Minzu University, Xining, China. Since then, much attention has been paid to this topic, but they mainly focus on undirected graphs and integral trees ...

Mathematics is the study of order, relation and pattern. From its origins in counting and measuring it has evolved in highly sophisticated and elegant ways to become the language now used to describe ...

Mathematics is the study of order, relation and pattern. From its origins in counting and measuring it has evolved in highly sophisticated and elegant ways to become the language now used to describe ...

Abstract: The paper describes an application that allows to visualize four-dimensional graphs of a complex variable function. Three coordinates of the graph are Cartesian, and fourth is the parametric ...

We present an example of a result in graph theory that is used to obtain a result in another branch of mathematics. More precisely, we show that the isomorphism of certain directed graphs implies that ...

Graph Neural Networks (GNNs) exploit signals from node features and the input graph topology to improve node classification task performance. However, these models tend to perform poorly on ...