Autor: Li, Hong - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On the Determinant of q-Distance Matrix of a Graph
Autorzy:: Li, Hong-Hai
Su, Li
Zhang, Jing
Powiązania:: https://bibliotekanauki.pl/articles/30147229.pdf
Data publikacji:: 2014-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: q-distance matrix
determinant
weighted graph
directed graph
Opis:: In this note, we show how the determinant of the q-distance matrix D_q(T) of a weighted directed graph G can be expressed in terms of the corresponding determinants for the blocks of G, and thus generalize the results obtained by Graham et al. [R.L. Graham, A.J. Hoffman and H. Hosoya, On the distance matrix of a directed graph, J. Graph Theory 1 (1977) 85-88]. Further, by means of the result, we determine the determinant of the q-distance matrix of the graph obtained from a connected weighted graph G by adding the weighted branches to G, and so generalize in part the results obtained by Bapat et al. [R.B. Bapat, S. Kirkland and M. Neumann, On distance matrices and Laplacians, Linear Algebra Appl. 401 (2005) 193- 209]. In particular, as a consequence, determinantal formulae of q-distance matrices for unicyclic graphs and one class of bicyclic graphs are presented.
Źródło:: Discussiones Mathematicae Graph Theory; 2014, 34, 1; 103-111
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number
Autorzy:: Su, Li
Li, Hong-Hai
Zhang, Jing
Powiązania:: https://bibliotekanauki.pl/articles/30148000.pdf
Data publikacji:: 2014-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: clique number
kite graph
signless Laplacian
spectral radius
Opis:: In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph $PK_{n-\omega,\omega}$ among all connected graphs with $n$ vertices and clique number $\omega$. In addition, we show that the spectral radius $\mu$ of $PK_{m,\omega}$ $(m\geq1)$ satisfies $$\frac{1}{2}(2\omega-1+\sqrt{4\omega^{2}-12\omega+17})\leq\mu\leq 2\omega-1.$$ More precisely, for $m>1$, $\mu$ satisfies the equation \[ \mu-\omega-\frac{\omega-1}{\mu-2\omega+3}=a_m\sqrt{\mu^2-4\mu}+\frac{1}{t_1}, \] where $a_m=\frac{1}{1-t_1^{2m+3}}$ and $t_{1}=\frac{\mu-2+\sqrt{(\mu-2)^{2}-4}}{2}$. At last the spectral radius $\mu(PK_{\infty,\omega})$ of the infinite graph $PK_{\infty,\omega}$ is also discussed.
Źródło:: Discussiones Mathematicae Graph Theory; 2014, 34, 1; 95-102
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: The Laplacian spectrum of some digraphs obtained from the wheel
Autorzy:: Su, Li
Li, Hong-Hai
Zheng, Liu-Rong
Powiązania:: https://bibliotekanauki.pl/articles/743220.pdf
Data publikacji:: 2012
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: digraph
Laplacian matrix
eigenvalue
wheel
Opis:: The problem of distinguishing, in terms of graph topology, digraphs with real and partially non-real Laplacian spectra is important for applications. Motivated by the question posed in [R. Agaev, P. Chebotarev, Which digraphs with rings structure are essentially cyclic?, Adv. in Appl. Math. 45 (2010), 232-251], in this paper we completely list the Laplacian eigenvalues of some digraphs obtained from the wheel digraph by deleting some arcs.
Źródło:: Discussiones Mathematicae Graph Theory; 2012, 32, 2; 255-261
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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