1965/01/01 by David C. Kay, Gary Chartrand · 3 citations
Computer Science · Mathematics · #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #Advanced Graph Theory Research #Mathematics #Combinatorics #Vertex (graph theory) #Distance #Graph #Distance-regular graph #Resistance distance #Path graph #Graph power #Discrete mathematics #Wheel graph #Line graph #Shortest path problem
paper · pdf · doi:10.4153/cjm-1965-034-0
openalex publication_date 1965/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
With every connected graph G there is associated a metric space M ( G ) whose points are the vertices of the graph with the distance between two vertices a and b defined as zero if a = b or as the length of any shortest arc joining a and b if a ≠ b . A metric space M is called a graph metric space if there exists a graph G such that M = M ( G ), i.e., if there exists a graph G whose vertex set can be put in one-to-one correspondence with the points of M in such a way that the distance between every two points of M is equal to the distance between the corresponding vertices of G .