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Halved Graphs

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For a connected bipartite graph πŸ‘ G
, the halved graph πŸ‘ G^+
and πŸ‘ G^-
are the two connected components of the graph distance-2 graph of πŸ‘ G
.

The following table summarizes some named graphs and halved graph pairs

graphhalved graphs
A graphtriangle graph πŸ‘ C_3
bipartite Kneser graph πŸ‘ H(7,3)
7-tetrahedral Johnson graph
πŸ‘ (4,6)
-cage		complete graph πŸ‘ K_(13)
complete bipartite graph πŸ‘ K_(n,n)
complete graph πŸ‘ K_n
πŸ‘ 2n
-crossed prism graph		πŸ‘ 2n
-circulant graph πŸ‘ Ci_(2n)(1,n-1,n)
crown graphcomplete graph πŸ‘ K_n
Nauru graphcirculant graph πŸ‘ Ci_(12)(1,2,5)
cubic symmetric graph πŸ‘ F_(026)A
13-Paley graph
cubic symmetric graph πŸ‘ F_(038)A
19-cyclotomic graph
cubic symmetric graph πŸ‘ F_(090)A
halved Foster graph
cubical graph πŸ‘ Q_3
tetrahedral graph
cycle graph πŸ‘ C_(2n)
cycle graph πŸ‘ C_n
Desargues graph5-triangular graph
Dyck graphShrikhande graph
Franklin graphcomplete graph πŸ‘ K_6
great rhombicosidodecahedral graphsnub dodecahedral graph
great rhombicuboctahedral graphsnub cubical graph
(8,1)-Hadamard graphcocktail party graph πŸ‘ K_(8Γ—2)
(12,1)-Hadamard graphcocktail party graph πŸ‘ K_(12Γ—2)
(16,1)-Hadamard graphcocktail party graph πŸ‘ K_(16Γ—2)
(16,2)-Hadamard graphcocktail party graph πŸ‘ K_(16Γ—2)
(16,3)-Hadamard graphcocktail party graph πŸ‘ K_(16Γ—2)
(16,4)-Hadamard graphcocktail party graph πŸ‘ K_(20Γ—2)
(20,1)-Hadamard graphcocktail party graph πŸ‘ K_(20Γ—2)
(20,2)-Hadamard graphcocktail party graph πŸ‘ K_(20Γ—2)
(20,3)-Hadamard graphcocktail party graph πŸ‘ K_(20Γ—2)
Heawood graphcomplete graph πŸ‘ K_7
H graphtriangle graph πŸ‘ C_3
bipartite double of the Hoffman-Singleton graphHoffman-Singleton graph complement
hypercube graph πŸ‘ Q_n
πŸ‘ n
-halved cube graph
Kummer graphcomplete graph πŸ‘ K_(16)
Tutte 8-cagegeneralized quadrangle GQ(2,2)
MΓΆbius-Kantor graph16-cell graph
πŸ‘ (2n+1)
-MΓΆbius ladder		circulant graph πŸ‘ Ci_(2n+1)(1,2)
Pappus graphcomplete tripartite graph πŸ‘ K_(3,3,3)
πŸ‘ 2n
-prism graph		πŸ‘ n
-antiprism graph
Reye configurationcomplete graph πŸ‘ K_(12)
rolling cube graphcocktail party graph πŸ‘ K_(6Γ—2)
square graphpath graph πŸ‘ P_2
sunlet graph πŸ‘ C_4 circledot K_1
diamond graph
sunlet graph πŸ‘ C_6 circledot K_1
2-SierpiΕ„ski gasket graph
tesseract graph16-cell graph
truncated octahedral graphicosahedral graph
utility graphtriangle graph πŸ‘ C_3

See also

Bipartite Double Graph, Double Graph, Graph Distance Graph, Halved Cube Graph

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References

Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance-Regular Graphs. New York: Springer-Verlag, pp. 25 and 438, 1989.

Referenced on Wolfram|Alpha

Halved Graphs

Cite this as:

Weisstein, Eric W. "Halved Graphs." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HalvedGraphs.html