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کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: Transactions on Combinatorics
- نوع مقاله: Journal Article
- کلمات کلیدی: Eigenvalue,Spectral radius,Graph operation,Distance signless Laplacian matrix,transmission regular graph
- چکیده:
- چکیده انگلیسی: Given a simple graph $G$, the distance signlesss Laplacian $D^{Q}(G)=Tr(G)+D(G)$ is the sum of vertex transmissions matrix $Tr(G)$ and distance matrix $D(G)$. In this paper, thanks to the symmetry of $D^{Q}(G)$, we obtain novel sharp bounds on the distance signless Laplacian eigenvalues of $G$, and in particular the distance signless Laplacian spectral radius. The bounds are expressed through graph diameter, vertex covering number, edge covering number, clique number, independence number, domination number as well as extremal transmission degrees. The graphs achieving the corresponding bounds are delineated. In addition, we investigate the distance signless Laplacian spectrum induced by Indu-Bala product, Cartesian product as well as extended double cover graph.
- انتشار مقاله: 12-12-1398
- نویسندگان: Abdollah Alhevaz,Maryam Baghipur,Shariefuddin Pirzada,Yilun Shang
- مشاهده
- جایگاه : پژوهشی
- مجله: Transactions on Combinatorics
- نوع مقاله: Journal Article
- کلمات کلیدی: diameter,Reversible rings,Zero-divisor graphs,Noetherian rings,Skew power series rings
- چکیده:
- چکیده انگلیسی: Let $R$ be an associative ring with identity and $Z^{ast}(R)$ be its set of non-zero zero-divisors. Zero-divisor graphs of rings are well represented in the literature of commutative and non-commutative rings. The directed zero-divisor graph of $R$, denoted by $Gamma{(R)}$, is the directed graph whose vertices are the set of non-zero zero-divisors of $R$ and for distinct non-zero zero-divisors $x,y$, $xrightarrow y$ is an directed edge if and only if $xy=0$. In this paper, we connect some graph-theoretic concepts with algebraic notions, and investigate the interplay between the ring-theoretical properties of a skew power series ring $R[[x;alpha]]$ and the graph-theoretical properties of its directed zero-divisor graph $Gamma(R[[x;alpha]])$. In doing so, we give a characterization of the possible diameters of $Gamma(R[[x;alpha]])$ in terms of the diameter of $Gamma(R)$, when the base ring $R$ is reversible and right Noetherian with an $alpha$-condition, namely $alpha$-compatible property. We also provide many examples for showing the necessity of our assumptions.
- انتشار مقاله: 20-10-1396
- نویسندگان: Ebrahim Hashemi,Marzieh Yazdanfar,Abdollah Alhevaz
- مشاهده