Boolean sum of graphs and reconstruction up to complementation
-
Jamel Dammak
,
Gérard Lopez
Abstract.
Let V be a set of cardinality v (possibly infinite). Two graphs G and 
with vertex set V are isomorphic up to complementation if is isomorphic to G or to the complement
of G. Let k be a non-negative integer. The graphs G and are k-hypomorphic up to complementation if for every k-element subset K of V, the induced subgraphs 
and 
are isomorphic up to complementation.
A graph G is k-reconstructible up to complementation if every
graph which is k-hypomorphic to G up to complementation is in fact isomorphic to G up to complementation.
We prove that a graph G has this property provided that 
. Moreover, under these conditions, if 
or 
, then
G and are the only graphs k-hypomorphic to G up to complementation. A description of pairs of graphs with the same 3-homogeneous subsets is a key ingredient in our proof.
© 2013 by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Masthead
- Using canonical dual frames in adaptive Richardson iterative method for solving operator equations
- On the existence of a resolvent of a class of singular mixed type differential operators in an unbounded domain
- A posteriori error estimates of a finite volume method based on the nonconforming rotated Q1 element for Stokes equations
- On weakly s-semipermutable subgroups of finite groups II
- Boolean sum of graphs and reconstruction up to complementation
Articles in the same Issue
- Masthead
- Using canonical dual frames in adaptive Richardson iterative method for solving operator equations
- On the existence of a resolvent of a class of singular mixed type differential operators in an unbounded domain
- A posteriori error estimates of a finite volume method based on the nonconforming rotated Q1 element for Stokes equations
- On weakly s-semipermutable subgroups of finite groups II
- Boolean sum of graphs and reconstruction up to complementation
