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Enumerations of vertex orders of almost Moore digraphs with selfrepeats
Baskoro E.T.a, Cholily Y.M.b, Miller M.c,d
a Combinatorial Mathematics Research Division, FMIPA, Institut Teknologi Bandung, Indonesia
b Universitas Muhammadiyah Malang, Indonesia
c School of Information Technology and Mathematical Sciences, University of Ballarat, Australia
d Department of Mathematics, University of West Bohemia, Czech Republic
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]An almost Moore digraph G of degree d > 1, diameter k > 1 is a diregular digraph with the number of vertices one less than the Moore bound. If G is an almost Moore digraph, then for each vertex u ∈ V (G) there exists a vertex v ∈ V (G), called repeat of u and denoted by r (u) = v, such that there are two walks of length ≤ k from u to v. The smallest positive integer p such that the composition rp (u) = u is called the order of u. If the order of u is 1 then u is called a selfrepeat. It is known that if G is an almost Moore digraph of diameter k ≥ 3 then G contains exactly k selfrepeats or none. In this paper, we propose an exact formula for the number of all vertex orders in an almost Moore digraph G containing selfrepeats, based on the vertex orders of the out-neighbours of any selfrepeat vertex. © 2007 Elsevier B.V. All rights reserved.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Almost Moore digraph,Selfrepeats,Vertex orders[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Almost Moore digraph,Selfrepeat[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text]Work partially supported by the Australian Research Council Grant ARC DP0450294.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1016/j.disc.2007.03.035[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]