Graphs and Combinatorics

, Volume 28, Issue 5, pp 637–652 | Cite as

Reconstructing a Graph from its Arc Incidence Graph

  • Stephen G. Hartke
  • Geir T. Helleloid
Original Paper


Introduced implicitly by Brualdi and Massey (Discret Math 122(1–3):51–58, 1993) in their work on the strong chromatic index of multigraphs, the arc incidence graph AI(G) of a graph G is defined as the square of the line graph of the incidence graph of G. We describe a linear-time algorithm for recognizing arc incidence graphs and reconstructing a graph with no isolated vertices from its arc incidence graph.


Arc incidence graph Incidence graph Incidence coloring conjecture Reconstruction Algorithm 


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Copyright information

© Springer 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of NebraskaLincolnUSA
  2. 2.Acuitus IncPaloAltoUSA

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