2014/10/29 by Narine N. Davtyan, Davtyan, Narine N., Arpine M. Khachatryan +3
Computer Science · Mathematics · #05C15 #05C78 #Advanced Algebra and Logic #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #cs.DM #math.CO #msc:05C15 #msc:05C78
paper · pdf · doi:10.48550/arxiv.1410.7927
arxiv created 2014/10/29 · openalex publication_date 2014/10/29 · arxiv updated 2014/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \textrmis 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.