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On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number

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Luo J., Zhu Z., Wan R.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 3

505-522

Let [...] φ(L(G))=det (xI−L(G))=∑k=0n(−1)kck(G)xn−k $\phi (L(G)) = \det (xI - L(G)) = \sum\nolimits_{k = 0}^n {( - 1)^k c_k (G)x^{n - k} } $ be the Laplacian characteristic polynomial of G. In this paper, we characterize the minimal graphs with the minimum Laplacian coefficients in 𝒢n,n+2(i) (the set of all tricyclic graphs with fixed order n and matching number i). Furthermore, the graphs with the minimal Laplacian-like energy, which is the sum of square roots of all roots on ϕ(L(G)), is also determined in 𝒢n,n+2(i).

Extremal Unicyclic Graphs With Minimal Distance Spectral Radius

100%

Lu H., Luo J., Zhu Z.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 4

735-749

The distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Let U (n,m) be the class of unicyclic graphs of order n with given matching number m (m ≠ 3). In this paper, we determine the extremal unicyclic graph which has minimal distance spectral radius in U (n,m) \ Cn.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Luo J.

2 Zhu Z.

1 Lu H.

1 Wan R.

1 2017

1 2014

Wyniki wyszukiwania

On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number

Extremal Unicyclic Graphs With Minimal Distance Spectral Radius