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Khachatryan Arpine ; Kamalian Rafayel

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Labeling ; interval spectrum ; induced subgraph

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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 ϕ : E(G) → {1, 2, . . . , |E(G)|} is called a labeling of the graph G. If G is a graph, x is its arbitrary vertex, and ϕ is its arbitrary labeling, then the set SG(x, ϕ) ≡ {ϕ(e)/e ∈ E(G), e is incident with x} is called a spectrum of the vertex x of the graph G at its labeling ϕ. For any graph G and its arbitrary labeling ϕ, a structure of the subgraph of G, induced by the subset of vertices of G with an interval spectrum, is described.

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#### Affiliation:

Ijevan Branch of Yerevan State University ; Institute for Informatics and Automation Problems