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On the number of spanning trees, the Laplacian eigenvalues, and the Laplacian Estrada index of subdivided-line graphs

100%

Shang Y.

Open Mathematics

2016

tom 14

nr 1

641-648

As a generalization of the Sierpiński-like graphs, the subdivided-line graph Г(G) of a simple connected graph G is defined to be the line graph of the barycentric subdivision of G. In this paper we obtain a closed-form formula for the enumeration of spanning trees in Г(G), employing the theory of electrical networks. We present bounds for the largest and second smallest Laplacian eigenvalues of Г(G) in terms of the maximum degree, the number of edges, and the first Zagreb index of G. In addition, we establish upper and lower bounds for the Laplacian Estrada index of Г(G) based on the vertex degrees of G. These bounds are also connected with the number of spanning trees in Г(G).

Codes and designs from triangular graphs and their line graphs

86%

Fish W., Kumwenda K., Mwambene E.

Open Mathematics

2011

tom 9

nr 6

1411-1423

For any prime p, we consider p-ary linear codes obtained from the span over $\mathbb{F}_p $ p of rows of incidence matrices of triangular graphs, differences of the rows and adjacency matrices of line graphs of triangular graphs. We determine parameters of the codes, minimum words and automorphism groups. We also show that the codes can be used for full permutation decoding.

Ograniczanie wyników

2 Open Mathematics

1 Fish W.

1 Kumwenda K.

1 Mwambene E.

1 Shang Y.

1 2016

1 2011

Wyniki wyszukiwania

On the number of spanning trees, the Laplacian eigenvalues, and the Laplacian Estrada index of subdivided-line graphs

Codes and designs from triangular graphs and their line graphs