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As you must have seen from my previous questions, I am mostly dealing with probabilistic maths so Graph is completely new to me. Still, I am trying to understand a paper that utilizes Graph theory.

I understand the Cartesian product of Graphs, my question is...Is the "Cartesian Product" and "Composition " of the graph the same thing?

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No, the composition of two graphs $G_1$ and $G_2$ is their Cartesian product plus an edge between every pair of vertices $(u_1,v_1)$ and $(u_2,v_2)$ where $u_1$ and $u_2$ are adjacent in $G_1$ and $v_1\neq v_2$.

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