Let G be a connected graph of order n and D(G) be its distance matrix. The distance eigenvalues of G are the eigenvalues of its distance matrix. Its distance eigenvalues and their multiplicities constitute the distanc...Let G be a connected graph of order n and D(G) be its distance matrix. The distance eigenvalues of G are the eigenvalues of its distance matrix. Its distance eigenvalues and their multiplicities constitute the distance spectrum of G. In this article, we give a complete description of the eigenvalues and the corresponding eigenvectors of a block matrix D_(NC). Further, we give a complete description of the eigenvalues and the corresponding eigenvectors of distance matrix of double neighbourhood corona graphs G^((S))· {G_1, G_2}, G^((Q))· {G_1, G_2}, G^((R))· {G_1, G_2},G^((T))· {G_1, G_2}, where G is a complete graph and G_1, G_2 are regular graphs.展开更多
It is well known that graph spectra store a lot of structural information about a graph,and it is more difficult to compute the spectra of corona graphs. In this paper two classes of new corona graphs,the corona-verte...It is well known that graph spectra store a lot of structural information about a graph,and it is more difficult to compute the spectra of corona graphs. In this paper two classes of new corona graphs,the corona-vertex of the subdivision graph G1◇G2and corona-edge of the subdivision graph G1☆G2were defined. Then,by using the coronal of a graph and some knowledge of linear algebra,the adjacency spectra and the signless Laplacian spectra of the two new graphs were explicitly computed in terms of the corresponding spectra of G1 and G2. As the application,some Aintegral graphs were constructed.展开更多
A subdivision vertex-edge corona G_1~S?(∪ G_3~E) is a graph that consists of S(G_1),|V(G_1)| copies of G_2 and |I(G_1)| copies of G_3 by joining the i-th vertex in V(G_1) to each vertex in the i-th copy of G_2 and i-...A subdivision vertex-edge corona G_1~S?(∪ G_3~E) is a graph that consists of S(G_1),|V(G_1)| copies of G_2 and |I(G_1)| copies of G_3 by joining the i-th vertex in V(G_1) to each vertex in the i-th copy of G_2 and i-th vertex of I(G_1) to each vertex in the i-th copy of G_3.In this paper, we determine the normalized Laplacian spectrum of G_1~S?(G_2~V∪ G_3~E) in terms of the corresponding normalized Laplacian spectra of three connected regular graphs G_1, G_2 and G_3. As applications, we construct some non-regular normalized Laplacian cospectral graphs. In addition, we also give the multiplicative degree-Kirchhoff index, the Kemeny's constant and the number of the spanning trees of G_1~S?(G_2~V∪ G_3~E) on three regular graphs.展开更多
<div style="text-align:justify;"> <span style="font-family:Verdana;">A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we cons...<div style="text-align:justify;"> <span style="font-family:Verdana;">A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we construct the corona between paths and second power of fan graphs and explain the necessary and sufficient conditions for this construction to be cordial.展开更多
基金Supported by the Dalian Science and Technology Project(Grant No.2015A11GX016)
文摘Let G be a connected graph of order n and D(G) be its distance matrix. The distance eigenvalues of G are the eigenvalues of its distance matrix. Its distance eigenvalues and their multiplicities constitute the distance spectrum of G. In this article, we give a complete description of the eigenvalues and the corresponding eigenvectors of a block matrix D_(NC). Further, we give a complete description of the eigenvalues and the corresponding eigenvectors of distance matrix of double neighbourhood corona graphs G^((S))· {G_1, G_2}, G^((Q))· {G_1, G_2}, G^((R))· {G_1, G_2},G^((T))· {G_1, G_2}, where G is a complete graph and G_1, G_2 are regular graphs.
基金National Natural Science Foundation of China(No.11361033)Natural Science Foundation of Gansu Province,China(No.1212RJZA029)
文摘It is well known that graph spectra store a lot of structural information about a graph,and it is more difficult to compute the spectra of corona graphs. In this paper two classes of new corona graphs,the corona-vertex of the subdivision graph G1◇G2and corona-edge of the subdivision graph G1☆G2were defined. Then,by using the coronal of a graph and some knowledge of linear algebra,the adjacency spectra and the signless Laplacian spectra of the two new graphs were explicitly computed in terms of the corresponding spectra of G1 and G2. As the application,some Aintegral graphs were constructed.
基金Supported by the Young Scholars Science Foundation of Lanzhou Jiaotong University(Grant Nos.20160142017004+3 种基金 2017021)the Education Foundation of Gansu Province(Grant No.2017A-021)the National Natural Science Foundation of China(Grant Nos.11461038 61163010)
文摘A subdivision vertex-edge corona G_1~S?(∪ G_3~E) is a graph that consists of S(G_1),|V(G_1)| copies of G_2 and |I(G_1)| copies of G_3 by joining the i-th vertex in V(G_1) to each vertex in the i-th copy of G_2 and i-th vertex of I(G_1) to each vertex in the i-th copy of G_3.In this paper, we determine the normalized Laplacian spectrum of G_1~S?(G_2~V∪ G_3~E) in terms of the corresponding normalized Laplacian spectra of three connected regular graphs G_1, G_2 and G_3. As applications, we construct some non-regular normalized Laplacian cospectral graphs. In addition, we also give the multiplicative degree-Kirchhoff index, the Kemeny's constant and the number of the spanning trees of G_1~S?(G_2~V∪ G_3~E) on three regular graphs.
文摘<div style="text-align:justify;"> <span style="font-family:Verdana;">A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we construct the corona between paths and second power of fan graphs and explain the necessary and sufficient conditions for this construction to be cordial.
