Character degree graphs constitute a powerful tool in the study of finite groups, encapsulating the interplay between group representation theory and graph theory. These graphs are constructed by ...

We consider the degrees of those irreducible characters of a group G whose kernels do not contain a given normal subgroup N. We show that if $N\subseteq G^{\prime ...

The degree distance of a connected graph G with vertex set V(G) is defined as $\sum\limits_{u \in V\left( G \right)} {{d_G}} \left( u \right){D_G}\left( u \right)$, where dG(u) is the degree of vertex ...

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections. “It’s a bit of a surprise, at least for me, that such a combination ...