5 - Further Properties
from Part III - Properties of the Shrikhande Graph
Published online by Cambridge University Press: 05 June 2026
Summary
In this chapter, we give the various properties and parameters of the Shrikhande graph; these have all been introduced earlier.
Vertices, edges, regularity The Shrikhande graph has 16 vertices and 48 edges. It is regular with degree 6. It is strongly regular: any two vertices have two common neighbours.
Symmetry The Shrikhande graph is vertex, edge and flag transitive. Its automorphism group is (Z4)2 : D12, of order 192, and has two orbits on non-edges.
Euler and Hamilton Since all vertices have even degree, the graph is Eulerian.
It is also Hamiltonian. Consider the description in Section 2.6. By using only four of the six types of edges given there
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- The Shrikhande GraphA Window on Discrete Mathematics, pp. 66 - 70Publisher: Cambridge University PressPrint publication year: 2026
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