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Distance-residual graphs

Primoz Luksic·Tomaz Pisanski
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Abstract

If we are given a connected finite graph $G$ and a subset of its vertices $V_{0}$, we define a distance-residual graph as a graph induced on the set of vertices that have the maximal distance from $V_{0}$. Some properties and examples of distance-residual graphs of vertex-transitive, edge-transitive, bipartite and semisymmetric graphs are shown. The relations between the distance-residual graphs of product graphs and their factors are shown.

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Primoz Luksic, Tomaz Pisanski. 2006-09-28. Distance-residual graphs. https://arxiv.org/abs/math/0609810

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