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Thread: Join of complete r-partite graphs

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    Join of complete r-partite graphs

    The join $\displaystyle G=G_1+ G_2$ of graphs $\displaystyle G_1$ and $\displaystyle G_2$ with disjoint point sets $\displaystyle V_1$ and $\displaystyle V_2$ and edge sets $\displaystyle X_1$ and $\displaystyle X_2$ is the graph union $\displaystyle G_1 \cup G_2$ together with all the edges joining $\displaystyle V_1$ and $\displaystyle V_2$.

    Suppose $\displaystyle G_1=G_2=$ the complete $\displaystyle r$-partite graph $\displaystyle K_{n, \ldots,n}$ then what is the graph $\displaystyle G=G_1+ G_2 ?$

    i.e, can we write $\displaystyle G$ by some well known graphs and their operations ?.
    Last edited by thippli; Jan 12th 2009 at 01:15 AM.
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