On the Laplacian coefficients of unicyclic graphs with prescribed matching number
نویسندگان
چکیده
منابع مشابه
On the Signless Laplacian Spectral Radius of Unicyclic Graphs with Fixed Matching Number
We determine the graph with the largest signless Laplacian spectral radius among all unicyclic graphs with fixed matching number.
متن کاملOn the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with Vertices and Pendent Vertices
Copyright q 2012 X. Pai and S. Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Let Φ G, λ det λIn − L G ∑n k 0 −1 ck G λn−k be the characteristic polynomial of the Laplacian matrix of a graph G of order n. In this paper, we g...
متن کاملThe Harmonic Index of Unicyclic Graphs with given Matching Number
The harmonic index of a graph G is defined as the sum of weights 2 d(u)+d(v) of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, we determine the graph with minimum harmonic index among all unicyclic graphs with a perfect matching. Moreover, the graph with minimum harmonic index among all unicyclic graphs with a given matching num...
متن کاملThe Signless Laplacian Estrada Index of Unicyclic Graphs
For a simple graph $G$, the signless Laplacian Estrada index is defined as $SLEE(G)=sum^{n}_{i=1}e^{q^{}_i}$, where $q^{}_1, q^{}_2, dots, q^{}_n$ are the eigenvalues of the signless Laplacian matrix of $G$. In this paper, we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$'s and then determine the unique unicyclic graph with maximum $SLEE$ a...
متن کاملUnicyclic Graphs with equal Laplacian Energy
We introduce a new operation on a class of graphs with the property that the Laplacian eigenvalues of the input and output graphs are related. Based on this operation, we obtain a family of Θ( √ n) noncospectral unicyclic graphs on n vertices with the same Laplacian energy.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2010.12.022