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Upper Bounds for the Exponents of Pseudo-symmetric Graphs by A. V. KNYAZEV is a Computer Science article available to read on EtoBox.

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A digraph with a vertex set V = {1,2,..., n} is called pseudo-symmetric if for the outdegree d Q (j) and the indegree d[r(j) of any vertex j E V the equality d 0 (j) = d\(j) is true. If for any j 6 V the equality d 0 (j) -d\(j) = 2 is true, then such a graph is said to be 2-diregular. The graph Γ is primitive if for any pair of its vertices i, j there exists a walk from i to j of length m > 0. The least such m is denoted by τ(Γ), and it is called the exponent of Γ. In Section 2 it is proved that for the exponent of any primitive 2-diregular graph Γ with girth (the length of the shortest elementary circuits) ρ > 2 the bound 7(Γ) 2, whose outdegrees and indegrees are not less than k > 3, the exponent is not greater than 5(n + p(2n -3))/(2(fc + 1)), and the precision of this bound is characterized.

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Author

A. V. KNYAZEV

Publisher

Walter de Gruyter GmbH

Published

1992

Language

EN

Field

Computer Science (Physical Sciences)