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enter image description hereI am unable to understand the graph operation defined in the following paper https://www.sciencedirect.com/science/article/pii/S0972860017301706.

Can someone kindly explain how the 1st graph operation is defined and how can we draw the graph?

I am attaching the screenshot where I am having trouble understanding. How is this new operation is defined and does it make sense?

How is this a generalization of Indu-Bala Product as referred in the paper? Please help

enter image description here

If someone can explain using any example for the graphs $G_1,G_2,G_3$ ,I will be grateful.

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  • $\begingroup$ The description becomes more clear to me if I assume G3 and G4 have k vertices each. Gerhard "Does This Produce Any Understanding?" Paseman, 2019.06.03. $\endgroup$ – Gerhard Paseman Jun 3 '19 at 15:57
  • $\begingroup$ @GerhardPaseman;can you kindly show how it is done for $G_1=P_2,G_3=C_4,G_2=P_3$? please $\endgroup$ – Math_Freak Jun 3 '19 at 16:03
  • $\begingroup$ Before I do, can you describe to me join of P2 and P3, and also Cartesian product of P3 and C4? Gerhard "Needs To Know Starting Point" Paseman, 2019.06.03. $\endgroup$ – Gerhard Paseman Jun 3 '19 at 16:25
  • $\begingroup$ @GerhardPaseman; yes i can describe $\endgroup$ – Math_Freak Jun 3 '19 at 17:34
  • $\begingroup$ @GerhardPaseman;i have added the solutions as image in the question,kindly check and please explain $\endgroup$ – Math_Freak Jun 3 '19 at 17:45

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