Upper bounds for the exponents of pseudo-symmetric graphs

A. V. KNYAZEV

doi:10.1515/dma.1992.2.3.293

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Upper bounds for the exponents of pseudo-symmetric graphs

KNYAZEV, A. V.

Follow Discrete Mathematics and Applications , Volume 2 (3) de Gruyter – Jan 1, 1992

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$-- A digraph with a vertex set V = {1,2,..., n} is called pseudo-symmetric if for the outdegree dQ(j) and the indegree d[r(j) of any vertex j E V the equality d0(j) = d\(j) is true. If for any j 6 V the equality d0(j) - d\(j) = 2 is true, then such a graph is said to be 2-diregular. The graph 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 (), and it is called the exponent of . In Section 2 it is proved that for the exponent of any primitive 2-diregular graph with girth (the length of the shortest elementary circuits) > 2 the bound 7() < n(p + l)/(2p -- 1) + p(n -- 2) -I- 5 holds, and the precision of this bound is characterized. In Section 3 it is proved that for a primitive pseudo-symmetric graph with girth > 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$

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Title: Upper bounds for the exponents of pseudo-symmetric graphs
Author(s): KNYAZEV, A. V.
Journal: Follow Discrete Mathematics and Applications , Volume 2 (3) de Gruyter – Jan 1, 1992
Publisher: Walter de Gruyter
ISSN: 0924-9265
eISSN: 1569-3929
D.O.I.: 10.1515/dma.1992.2.3.293
Publisher site: Get PDF