Jahangir Graph

The Jahangir graph J_(n,m) is a kind of generalized wheel graph with consisting of mn circular vertices and a central vertex connected to every mth vertex around the circle.


This class of graphs is named after the figure illustrated above corresponding to J_(2,8) which appears on the tomb of Nur-ud-din Muhammad Salim, known by his imperial name, Jahangir. Jahangir was the fourth Mughal Emperor who ruled from 1605-1627. His tomb is located 5 kilometer northwest of Lahore, Pakistan along the banks of the River Ravi (Mojdeh and Ghameshlou 2007).

Jahangir graphs J_(n,m) are unit-distance and matchstick graphs for n=1,m=6 (the wheel graph W_7) and all n>1.

Special cases are summarized in the following table.

Jahangir graphs are implemented in the Wolfram Language as GraphData[{"Jahangir", {n, m}}].

See also

Gear Graph, Wheel Graph

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Ali, K.; Baskoro, E. T.; Tomescu, I. "On the Ramsey Numbers for Paths and Generalized Jahangir Graphs J_(s,m)." Bull. Math. Soc. Sci. Math. Roumanie 51, 177-182, 2008.Kok, J. "A Note on J-Colouring of Jahangir Graphs." 28 Jun 2018., D. A. and Ghameshlou, A. N. "Domination in Jahangir Graph J_(2,m)." Int. J. Contemp. Math. Sci. 2, 1193-1199, 2007.Munir, M.; Nazeer, W.; Kang, S. M.; Qureshi, M. I.; Nizami, A. R.; Kwun, Y. C. "Some Invariants of Jahangir Graphs." Symmetry 9, No. 17, 15 pp., 2017.Tomescu, I. and Javid, I. "On the Metrix Dimension of the Jahangir Graph." Bull. Math. Soc. Sci. Math. Roumainie 50, 371-376, 2007.

Cite this as:

Weisstein, Eric W. "Jahangir Graph." From MathWorld--A Wolfram Web Resource.

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