Subgraph summability number of paths and cycles

David V. Cochran, Raj J. Doshi, Miriam R. Larson-Koester, Richard G. Ligo, Sivaram K. Narayan, Jordan D. Webster

Research output: Contribution to journalArticlepeer-review


A vertex labeling of a graph G is a mapping α: V (G) → N, assigning a positive integer value to each vertex. With this we can consider labels of connected induced subgraphs G[U] for U ⊆ V (G), and define α(G[U]) = ∑u∈U α(u). The subgraph summability number of a connected graph G is the largest integer σ(G) so that label sums of connected induced subgraphs cover the integers 1 through σ(G) for some vertex labeling of G. We investigate subgraph summability labelings for paths and cycles and provide upper and lower bounds.

Original languageEnglish
Pages (from-to)135-143
Number of pages9
JournalAKCE International Journal of Graphs and Combinatorics
Issue number2
StatePublished - 2012


  • Cycles
  • Cyclic difference sets
  • Graph labeling
  • Paths
  • Subgraph summability number


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