On the Structure of Digraphs with Order Close to the Moore Bound

Baskoro, Edy Tri; Miller, Mirka; Plesník, Ján

doi:10.1007/s003730050019

Cited by 23 publications

(25 citation statements)

References 15 publications

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“…Recall that a Moore graph or digraph is a graph or digraph that meets the Moore bound or directed Moore bound, respectively. Let us refer to the survey [30] and articles [8,[10][11][12][13] for more information pertaining to the Moore graphs.…”

Section: Resultsmentioning

confidence: 99%

Distances of Centroid Sets in a Graph-Based Construction for Information Security Applications

et al. 2015

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The aim of this paper is to prove that, for every balanced digraph, in every incidence semiring over a semifield, each centroid set J of the largest distance also has the largest weight, and the distance of J is equal to its weight. This result is surprising and unexpected, because examples show that distances of arbitrary centroid sets in incidence semirings may be strictly less than their weights. The investigation of the distances of centroid sets in incidence semirings of digraphs has been motivated by the information security applications of centroid sets.

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Section: Resultsmentioning

confidence: 99%

Distances of Centroid Sets in a Graph-Based Construction for Information Security Applications

et al. 2015

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“…If we have u = r(u), thus u has order 1 with respect to r, u is said to be a selfrepeat. If there is a selfrepeat in G, then there are exactly k selfrepeats, which lie on a k-cycle, see [3].…”

Section: Lemma 11 ([4]mentioning

confidence: 99%

Subdigraphs of almost Moore digraphs induced by fixpoints of an automorphism

Sillasen

2015

ejgta

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The degree/diameter problem for directed graphs is the problem of determining the largest possible order for a digraph with given maximum out-degree d and diameter k. An upper bound is given by the Moore bound M (d, k) = In this paper we will look at the structure of subdigraphs of almost Moore digraphs, which are induced by the vertices fixed by some automorphism ϕ. If the automorphism fixes at least three vertices, we prove that the induced subdigraph is either an almost Moore digraph or a diregularAs it is known that almost Moore digraphs have an automorphism r, these results can help us determine structural properties of almost Moore digraphs, such as how many vertices of each order there are with respect to r. We determine this for d = 4 and d = 5, where we prove that except in some special cases, all vertices will have the same order.

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“…A Moore digraph is a digraph that meets the directed Moore bound. Let us refer to the survey [21] and articles [15,16,17,18,19] for more information and previous results on the Moore digraphs. Another important and well known class of digraphs is that of digraphs with edge antimagic labelling (cf.…”

Section: Examples and Open Questionsmentioning

confidence: 99%

Ideal basis in constructions defined by directed graphs

Abawajy

Kelarev

Ryan³

2015

ejgta

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The present article continues the investigation of visible ideal bases in constructions defined using directed graphs. Our main theorem establishes that, for every balanced digraph D and each idempotent semiring R with 1, the incidence semiring I D (R) of the digraph D has a convenient visible ideal basis B D (R). It also shows that the elements of B D (R) can always be used to generate two-sided ideals with the largest possible weight among the weights of all two-sided ideals in the incidence semiring.

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On the Structure of Digraphs with Order Close to the Moore Bound

Cited by 23 publications

References 15 publications

Distances of Centroid Sets in a Graph-Based Construction for Information Security Applications

Distances of Centroid Sets in a Graph-Based Construction for Information Security Applications

Subdigraphs of almost Moore digraphs induced by fixpoints of an automorphism

Ideal basis in constructions defined by directed graphs

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