Trees with Four and Five Distinct Signless Laplacian Eigenvalues
2019 ◽
Vol 25
(3)
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pp. 302-313
Keyword(s):
Let $G$ be a simple graph with vertex set $V(G)=\{v_1, v_2, \cdots, v_n\}$ andedge set $E(G)$.The signless Laplacian matrix of $G$ is the matrix $Q=D+A$, such that $D$ is a diagonal matrix%, indexed by the vertex set of $G$ where%$D_{ii}$ is the degree of the vertex $v_i$ and $A$ is the adjacency matrix of $G$.% where $A_{ij} = 1$ when there%is an edge from $i$ to $j$ in $G$ and $A_{ij} = 0$ otherwise.The eigenvalues of $Q$ is called the signless Laplacian eigenvalues of $G$ and denoted by $q_1$, $q_2$, $\cdots$, $q_n$ in a graph with $n$ vertices.In this paper we characterize all trees with four and five distinct signless Laplacian eigenvalues.
2016 ◽
Vol 5
(2)
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pp. 132
Keyword(s):
2018 ◽
Vol 34
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pp. 191-204
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2011 ◽
Vol 03
(02)
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pp. 185-191
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2019 ◽
Vol 12
(01)
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pp. 2050006
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Keyword(s):
2019 ◽
Vol 13
(06)
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pp. 2050113
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2015 ◽
Vol 30
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pp. 605-612
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