Reliability and fault tolerance are two important parameters of an interconnection network. As a topology structure of interconnection networks, the godan graph <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7025_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">$EA_n$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <msub> <mi>A</mi> <mi>n</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> has many good properties, such as regularity, high connectivity, and vertex-transitivity. Ren and Wang [<CitationRef CitationID="CR13">13</CitationRef>] gave various connectivities of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7025_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">$EA_n$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <msub> <mi>A</mi> <mi>n</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>, for example, nature connectivity, 2-good neighbor connectivity, 2-extra connectivity. In this paper, we give some other connectivities of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7025_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">$EA_n$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <msub> <mi>A</mi> <mi>n</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>: the g-component edge connectivity for <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7025_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="72" /> </InlineMediaObject> <EquationSource Format="TEX">$3\le g\le 5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3</mn> <mo>≤</mo> <mi>g</mi> <mo>≤</mo> <mn>5</mn> </mrow> </math></EquationSource> </InlineEquation>, the h-extra edge connectivity for <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7025_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="73" /> </InlineMediaObject> <EquationSource Format="TEX">$1\le h\le 3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>h</mi> <mo>≤</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>, and the (edge) neighbor connectivity.

Conditional connectivities of the n-dimensional godan graph

期刊论文
发表日期：

2025年2月17日

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Xiaohui Hua,
Yonghao Lai

摘要

Reliability and fault tolerance are two important parameters of an interconnection network. As a topology structure of interconnection networks, the godan graph $EA_n$ $E A_{n}$ has many good properties, such as regularity, high connectivity, and vertex-transitivity. Ren and Wang [13] gave various connectivities of $EA_n$ $E A_{n}$ , for example, nature connectivity, 2-good neighbor connectivity, 2-extra connectivity. In this paper, we give some other connectivities of $EA_n$ $E A_{n}$ : the g-component edge connectivity for $3\le g\le 5$ $3 \leq g \leq 5$ , the h-extra edge connectivity for $1\le h\le 3$ $1 \leq h \leq 3$ , and the (edge) neighbor connectivity.