Graph Strong Product
المؤلف:
Alon, N. and Lubetzky, E
المصدر:
"The Shannon Capacity of a Graph and the Independence Numbers of Its Powers." IEEE Trans. Inform. Th. 52,
الجزء والصفحة:
...
13-4-2022
1731
Graph Strong Product
The graph strong product is a graph product variously denoted ![G□AdjustmentBox[x, BoxMargins -> <span style=]()
{{-0.65, 0.13913}, {-0.5, 0.5}}, BoxBaselineShift -> -0.1]H" src="https://mathworld.wolfram.com/images/equations/GraphStrongProduct/Inline1.svg" style="height:22px; width:52px" />, 
(Alon, and Lubetzky 2006), or 
(Beineke and Wilson 2004, p. 104) defined by the adjacency relations (
and 
) or (
and 
) or (
and 
).
In other words, the graph strong product of two graphs 
and 
has vertex set 
and two distinct vertices 
and 
are connected iff they are adjacent or equal in each coordinate, i.e., for ![i in <span style=]()
{1,2}" src="https://mathworld.wolfram.com/images/equations/GraphStrongProduct/Inline15.svg" style="height:22px; width:70px" />, either 
or 
, where 
is the edge set of 
.
REFERENCES
Alon, N. and Lubetzky, E. "The Shannon Capacity of a Graph and the Independence Numbers of Its Powers." IEEE Trans. Inform. Th. 52, 2172-2176, 2006.
Beineke, L. W. and Wilson, R. J. (Eds.). Topics in Algebraic Graph Theory. New York: Cambridge University Press, p. 104, 2004.
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