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 ...

A signed bipartite graph G(U,V) is a bipartite graph in which each edge is assigned a positive or a negative sign. The signed degree of a vertex x in G(U, V) is the number of positive edges incident ...

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