Combinatorial Dual Graph
المؤلف:
Harary, F
المصدر:
Graph Theory. Reading, MA: Addison-Wesley
الجزء والصفحة:
pp. 113-115
8-4-2022
2198
Combinatorial Dual Graph
Let 
be the cycle rank of a graph 
, 
be the cocycle rank, and the relative complement 
of a subgraph 
of 
be defined as that subgraph obtained by deleting the lines of 
. Then a graph 
is a combinatorial dual of 
if there is a one-to-one correspondence between their sets of lines such that for any choice 
and 
of corresponding subsets of lines,
where 
is the subgraph of 
with the line set 
.
Whitney showed that the geometric dual graph and combinatorial dual graph are equivalent (Harary 1994, p. 115), and so may simply be called "the" dual graph. Also, a graph is planar iff it has a combinatorial dual (Harary 1994, p. 115).
REFERENCES
Harary, F. Graph Theory. Reading, MA: Addison-Wesley, pp. 113-115, 1994.
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