Graph Sum
GraphSum
The graph sum of graphs G and H is the graph with adjacency matrix given by the sum of adjacency matrices of G and H. A graph sum is defined when the orders of G and H are the same. The example illustrated above shows the graph sum K_5+C_5 of the pentatope graph K_5 and the cycle graph C_5, corresponding to adjacency matrices
![画像: [0 1 1 1 1; 1 0 1 1 1; 1 1 0 1 1; 1 1 1 0 1; 1 1 1 1 0]+[0 1 0 0 1; 1 0 1 0 0; 0 1 0 1 0; 0 0 1 0 1; 1 0 0 1 0]=[0 2 1 1 2; 2 0 2 1 1; 1 2 0 2 1; 1 1 2 0 2; 2 1 1 2 0].](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/GraphSum/NumberedEquation1.svg){kind=link}
Graph sums can be computed in the Wolfram Language using GraphSum [g, h].
See also
Graph Difference, Graph Join, Graph UnionExplore with Wolfram|Alpha
WolframAlpha
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References
Beineke, L. W. and Wilson, R. J. (Eds.). Topics in Algebraic Graph Theory. New York: Cambridge University Press, p. 104, 2004.Skiena, S. "Sum and Difference." §4.1.2 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 131, 1990.Referenced on Wolfram|Alpha
Graph SumCite this as:
Weisstein, Eric W. "Graph Sum." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GraphSum.html