Ball and Coxeter (1987, pp. 277-278) define the ladder graph , here called the ladder rung graph, of order as the graph union of copies of the path graph .
The -ladder rung graph is isomorphic to the Haar graph and to the Knödel graph . Kneser graphs of the form are ladder rung graphs of order , where is a central binomial coefficient.
The graph complement of is the cocktail party graph .
If the restriction in the I graph is loosened, corresponds to .
Ladder rung graphs are trivially unit-distance graphs.
has chromatic polynomial, independence polynomial, and matching polynomial are given by
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(2)
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with corresponding recurrence equations
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(5)
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(6)
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The bipartite double graph of is .