Incidence graphs constructed from t-designs
Xu Yang, Weijun Liu, Henry X. Liu, Lihua Feng · Applicable Analysis and Discrete Mathematics · 2016
Let D be a non-trivial simple t-design. In this paper, for 1 ≤ s ≤ t, we generalize the concept of the incidence graph of D and construct a new bi- partite regular graph Γ. We obtain that the edge-transitivity of the graph Γ is equivalent to the s-ag-transitivity of the design D. We then, for s = 2, classify the semisymmetric graphs among the graphs Γ constructed from bi-planes and triplanes. Finally, we study the connectedness and the energy of incidence graphs. Several open problems are proposed, one of which asks whether the incidence graphs have large vertex-connectivity.