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- W2890218256 abstract "Abstract In this paper, we introduce the notion of perfect matching property for a k-partition of vertex set of given graph. We consider nontrivial graphs G and G P k , the k-complement of graph G with respect to a kpartition of V(G), to prove that A(G)A(G P k ) is realizable as a graph if and only if P satis_es perfect matching property. For A(G)A(G P k ) = A(Γ) for some graph Γ, we obtain graph parameters such as chromatic number, domination number etc., for those graphs and characterization of P is given for which G P k and Γ are isomorphic. Given a 1-factor graph G with 2n vertices, we propose a partition P for which G P k is a graph of rank r and A(G)A(G P k ) is graphical, where n ≤ r ≤ 2n. Motivated by the result of characterizing decomposable Kn,n into commuting perfect matchings [2], we characterize complete k-partite graph K n1,n2,...,nk which has a commuting decomposition into a perfect matching and its k-complement." @default.
- W2890218256 created "2018-09-27" @default.
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- W2890218256 date "2018-08-01" @default.
- W2890218256 modified "2023-09-27" @default.
- W2890218256 title "Commuting decomposition of K<sub>n1,n2,...,nk</sub> through realization of the product A(G)A(G<sup>P</sup> <sub>k</sub> )" @default.
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- W2890218256 doi "https://doi.org/10.1515/spma-2018-0028" @default.
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