A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.

The incidence matrices of various graphs are considered. By reordering the points, the bandwidth can be changed. In the cases of rectangular grids in the plane or cubic grids in three dimensions, the ...

This paper is mainly concerned with the realizability of a set of n integers as the degrees of vertices of an n-vertex linear graph. Other related problems, such as when a set of integers is ...

Gallai–Ramsey number: The minimum number of vertices in a complete graph such that every Gallai colouring using a given number of colours yields a monochromatic copy of a specified subgraph.

These methods involve assigning numerical labels to the vertices and edges of a graph to generate unique weight sums, thereby distinguishing each element’s role within the structure.

A next-generation graph-relational database (DB) system has been developed in South Korea. If this system is applied in ...