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some inequalities involving the distance signless laplacian eigenvalues of graphs
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نویسنده
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alhevaz abdollah ,baghipur maryam ,pirzada shariefuddin ,shang yilun
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منبع
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transactions on combinatorics - 2021 - دوره : 10 - شماره : 1 - صفحه:9 -29
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چکیده
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Given a simple graph 𝐺, the distance signlesss laplacian 𝐷^𝑄(𝐺) = 𝑇 r(𝐺) + 𝐷(𝐺) is the sum of vertex transmissions matrix 𝑇 r(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.
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کلیدواژه
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distance signless laplacian matrix ,eigenvalue ,transmission regular graph ,spectral radius ,graph operation
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آدرس
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shahrood university of technology, faculty of mathematical sciences, iran, university of hormozgan, department of mathematics, iran, university of kashmir, department of mathematics, india, northumbria university, department of computer and information sciences, uk
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پست الکترونیکی
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yilun.shang@northumbria.ac.uk
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Authors
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