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- W3059396209 abstract "For interconnection network losing processors, it is considerable to calculate the number of vertices in the maximal component in the surviving network. Moreover, the component connectivity is a significant indicator for reliability of a network in the presence of failing processors. In this article, we first prove that when a set <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$M$</tex-math></inline-formula> of at most <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$3n-7$</tex-math></inline-formula> processors is deleted from an <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$n$</tex-math></inline-formula> -star graph, the surviving graph has a large component of size greater or equal to <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$n!-|M|-3$</tex-math></inline-formula> . We then prove that when a set <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$M$</tex-math></inline-formula> of at most <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$4n-9$</tex-math></inline-formula> processors is deleted from an <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$n$</tex-math></inline-formula> -star graph, the surviving graph has a large component of size greater or equal to <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$n!-|M|-5$</tex-math></inline-formula> . Finally, we also calculate the <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$r$</tex-math></inline-formula> -component connectivity of the <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$n$</tex-math></inline-formula> -star graph for <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$2leq rleq 5$</tex-math></inline-formula> ." @default.
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- W3059396209 date "2022-09-01" @default.
- W3059396209 modified "2023-10-17" @default.
- W3059396209 title "Strong Reliability of Star Graphs Interconnection Networks" @default.
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