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On the structure of digraphs with order close to the moore bound
Baskoro E.T.a, Miller M.b, Plesnik J.c
a Department of Mathematics, Institut Teknologi Bandung (ITB), Indonesia
b Department of Computer Science, University of Newcastle, Australia
c Dept. Numer. Optimization Methods, Faculty of Mathematics and Physics, Comenius University, Slovakia
[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]The Moore bound for a diregular digraph of degree d and diameter k is Md,k = 1 + d + ⋯+ dk. It is known that digraphs of order Md,k do not exist for d > 1 and k > 1 ([24] or [6]). In this paper we study digraphs of degree d, diameter k and order Md,k – 1, denoted by (d,k)-digraphs. Miller and Fris showed that (2, k)-digraphs do not exist for k ≥ 3 [22]. Subsequently, we gave a necessary condition of the existence of (3,k)-digraphs, namely, (3,k)-digraphs do not exist if k is odd or if k + 1 does not divide 9/2 (3k – 1) [3]. The (d, 2)-digraphs were considered in [4]. In this paper, we present further necessary conditions for the existence of (d, k)-digraphs. In particular, for d, k ≥ 3, we show that a (d, k)-digraph contains either no cycle of length k or exactly one cycle of length k. © Springer-Verlag 1998.[/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][/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][/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][/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/10.1007/s003730050019[/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]