A. A. Mironov Dokl. Math. , vol.54 No.3 , 01.1996 , p. 965-968, language: английский ISSN 1064-5624  Аннотация A weighted (labelled) graph $G= (V,E)$ with a fixed set of vertices $\{u_1,u_2,\dots, u_n\}$ is defined to be uniform generalized if for weights $c_{ij}$ of edges $u_iu_j$ and weighted degrees $\text{w}\deg u_i$ of vertices the following holds: $c_{ij}= c_{pq}$ if $\text{w}\deg u_i= \text{w}\deg u_p$ and $\text{w}\deg u_j= \text{w}\deg u_q$ and $c_{ij}\ge c_{pq}$ if $\text{w}\deg u_i\ge \text{w}\deg u_p$, $\text{w}\deg u_j\ge \text{w}\deg u_q$. The paper presents a method of investigation of uniform generalized graphs as "linear combinations" of simpler graphs, called extremal, which are completely determined by their weighted degrees.  Ключевые слова weighted graph; generalized graphs; weighted degrees

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