A graph card, or simply card, of a graph is one of the one-vertex-deleted vertex-induced
subgraphs
occurring in the graph deck of
, 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
with vertex 3 highlighted, together with the corresponding graph card
obtained by deleting vertex 3 and all edges incident to
it.
Graph Card
See also
Graph Deck, Graph Reconstruction Conjecture, Vertex-Induced SubgraphExplore with Wolfram|Alpha
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