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This book is based on Graph Theory courses taught by P.A. Petrosyan, V.V. Mkrtchyan and R.R. Kamalian at Yerevan State University., 215 pages (in Armenian)

The sets of vertices and edges of an undirected, simple, finite, connected graph $G$ are denoted by $V(G)$ and $E(G)$, respectively. An arbitrary nonempty finite subset of consecutive integers is called an interval. An injective mapping $\varphi:E(G)\rightarrow \{1,2,...,|E(G)|\}$ is called a labeling of the graph $G$. If $G$ is a graph, $x$ is its arbitrary vertex, and $\varphi$ is its arbitrary labeling, then the set $S_G(x,\varphi)\equiv\{\varphi(e)/ e\in E(G), e \textrm{is incident with} x$\} is called a spectrum of the vertex $x$ of the graph $G$ at its labeling $\varphi$. For any graph $G$ and its arbitrary labeling $\varphi$, a structure of the subgraph of $G$, induced by the subset of vertices of $G$ with an interval spectrum, is described.

A necessary and sufficient condition is found for a graph $G$, which satisfies the equality $��_{21}(G)=|V(G)|$.

The existence of a partition of the common set of the vertices of two forests into two subsets, when difference of their capacities in the neighborhood of each vertex of each forest not greater than 2 is proved, and an example, which shows that improvement of the specified constant is impossible is brought., Comment: 3 pages