Merging the A-and Q-spectral theories
Let G be a graph with adjacency matrix A(G), and let D(G) be the diagonal matrix of the degrees of G: The signless Laplacian Q(G) of G is defined as Q(G):= A(G) +D(G). Cvetkovic called the study of the adjacency matrix the A-spectral theory, and the study of the signless Laplacian{the Q-spectral the...
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| Published in | Applicable analysis and discrete mathematics Vol. 11; no. 1; pp. 81 - 107 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.04.2017
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| Online Access | Get full text |
| ISSN | 1452-8630 2406-100X 2406-100X |
| DOI | 10.2298/AADM1701081N |
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| Summary: | Let G be a graph with adjacency matrix A(G), and let D(G) be the
diagonal matrix of the degrees of G: The signless Laplacian Q(G) of G is
defined as Q(G):= A(G) +D(G). Cvetkovic called the study of the adjacency
matrix the A-spectral theory, and the study of the signless Laplacian{the
Q-spectral theory. To track the gradual change of A(G) into Q(G), in this
paper it is suggested to study the convex linear combinations A_ (G) of A(G)
and D(G) defined by A? (G) := ?D(G) + (1 - ?)A(G), 0 ? ? ? 1. This study
sheds new light on A(G) and Q(G), and yields, in particular, a novel
spectral Tur?n theorem. A number of open problems are discussed.
nema |
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| ISSN: | 1452-8630 2406-100X 2406-100X |
| DOI: | 10.2298/AADM1701081N |