Tree-like isometric subgraphs of hypercubes
نویسندگان
چکیده
منابع مشابه
Tree-like isometric subgraphs of hypercubes
Tree-like isometric subgraphs of hypercubes, or tree-like partial cubes as we shall call them, are a generalization of median graphs. Just as median graphs they capture numerous properties of trees, but encompass a larger class of graphs that may be easier to recognize than the class of median graphs. We investigate the structure of tree-like partial cubes, characterize them, and provide exampl...
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Isometric subgraphs of hypercubes are known as partial cubes. Edge-critical partial cubes are introduced as the partial cubes G for which G e is not a partial cube for any edge e of G. An expansion theorem is proved by means of which one can generate many edge-critical partial cubes. Edge-critical partial cubes are characterized among the Cartesian product graphs. We also show that the 3-cube a...
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Let d(G, k) be the number of pairs of vertices of a graph G that are at distance k, λ a real (or complex) number, and Wλ(G) = ∑ k≥1 d(G, k) k . It is proved that for a partial cube G, Wλ+1(G) = |F|Wλ(G)− ∑ F∈F Wλ(G\F ), where F is the partition of E(G) induced by the Djoković-Winkler relation Θ. This result extends previously known result for trees and implies several relations for distance-bas...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2003
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1199