### AIMS Mathematics

2020, Issue 6: 7214-7233. doi: 10.3934/math.2020461
Research article

# Central vertex join and central edge join of two graphs

• Received: 06 July 2020 Accepted: 30 August 2020 Published: 14 September 2020
• MSC : 05C50

• The central graph $C(G)$ of a graph $G$ is obtained by sub dividing each edge of $G$ exactly once and joining all the nonadjacent vertices in $G$. In this paper, we compute the adjacency, Laplacian and signless Laplacian spectra of central graph of a connected regular graph. Also, we define central vertex join and central edge join of two graphs and calculate their adjacency spectrum, Laplacian spectrum and signless Laplacian spectrum. As an application, some new families of integral graphs and cospectral graphs are constructed. In addition to that the Kirchhoff index and number of spanning trees of the new joins are determined.

Citation: Jahfar T K, Chithra A V. Central vertex join and central edge join of two graphs[J]. AIMS Mathematics, 2020, 5(6): 7214-7233. doi: 10.3934/math.2020461

### Related Papers:

• The central graph $C(G)$ of a graph $G$ is obtained by sub dividing each edge of $G$ exactly once and joining all the nonadjacent vertices in $G$. In this paper, we compute the adjacency, Laplacian and signless Laplacian spectra of central graph of a connected regular graph. Also, we define central vertex join and central edge join of two graphs and calculate their adjacency spectrum, Laplacian spectrum and signless Laplacian spectrum. As an application, some new families of integral graphs and cospectral graphs are constructed. In addition to that the Kirchhoff index and number of spanning trees of the new joins are determined. ###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142 1.427 1.6

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