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Graph Card


GraphCard

A graph card, or simply card, of a graph G is one of the one-vertex-deleted vertex-induced subgraphs G-v occurring in the graph deck of G, usually considered up to graph isomorphism. If two deleted vertices give isomorphic subgraphs, the corresponding card occurs in the deck with multiplicity, since the graph deck is a multiset. The terminology is by analogy with a card in a deck of playing cards. The illustration above shows a graph G with vertex 3 highlighted, together with the corresponding graph card G-3 obtained by deleting vertex 3 and all edges incident to it.


See also

Graph Deck, Graph Reconstruction Conjecture, Vertex-Induced Subgraph

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References

Bondy, J. A. and Hemminger, R. L. "Graph Reconstruction--A Survey." J. Graph Th. 1, 227-268, 1977.

Cite this as:

Weisstein, Eric W. "Graph Card." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GraphCard.html

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