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- W4319586632 abstract "We present a simple recurrence for the surface area of the ( <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$n, k$</tex> ) -star graph, <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$0 < k < n$</tex> , i.e., the number of nodes at a certain distance from the identity node in the graph, an important parameter for interconnection networks in parallel computing. The family of the ( <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$n, k$</tex> ) -star graphs includes several popular interconnection networks such as the star graph and the alternating group network. Previously, a surface area recurrence has been obtained for a special case, e.g., when <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$k=n-1$</tex> , in the family of ( <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$n, k$</tex> ) -star. Our recurrence gives one single recurrence for all graphs in the family, thus completely solving the surface area of ( <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$n, k$</tex> ) -star for all <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$0 < k < n$</tex> . Compared to explicit surface area formulas previously obtained through complicated and involved combinatorial analysis and generating function approach, our derivation is more elementary and our recurrence gives a way to compute the surface area of the ( <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$n, k$</tex> ))-star efficiently." @default.
- W4319586632 created "2023-02-09" @default.
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- W4319586632 date "2022-11-01" @default.
- W4319586632 modified "2023-09-27" @default.
- W4319586632 title "A Recurrence for the Surface Area of the ($n, k$)-Star Graph" @default.
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- W4319586632 doi "https://doi.org/10.1109/candar57322.2022.00011" @default.
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