Jump symmetric n-sigraphs
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An n-tuple (a₁, a₂, ..., an) is symmetric, if ak = an−k+₁, 1 ≤ k ≤ n. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair Sn = (G, δ) (Sn = (G, μ)), where G = (V,E) is a graph called the underlying graph of Sn and δ : E → Hn (μ : V → Hn) is a function. Analogous to the concept of Jump sigraph of a sigraph, we define Jump symmetric n-sigraph of a symmetric n-sigraph. Introducing two notions of balance in symmetric n-sigraphs and some notions of complements we characterize the symmetric n-sigraphs which are switching equivalent to their Jump symmetric n-sigraphs.
Abstract
An n-tuple (a₁, a₂, ..., an) is symmetric, if ak = an−k+₁, 1 ≤ k ≤ n. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair Sn = (G, δ) (Sn = (G, μ)), where G = (V,E) is a graph called the underlying graph of Sn and δ : E → Hn (μ : V → Hn) is a function. Analogous to the concept of Jump sigraph of a sigraph, we define Jump symmetric n-sigraph of a symmetric n-sigraph. Introducing two notions of balance in symmetric n-sigraphs and some notions of complements we characterize the symmetric n-sigraphs which are switching equivalent to their Jump symmetric n-sigraphs.
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