@Article{AAM-34-4, author = {Xianzhang, Wu and Shen, Lili}, title = {On the Normalized Laplacian Spectrum of a New Join of Two Graphs}, journal = {Annals of Applied Mathematics}, year = {2018}, volume = {34}, number = {4}, pages = {407--415}, abstract = {

Given graphs $G_1$ and $G_2,$ we define a graph operation on $G_1$ and $G_2$, namely the $SSG$-vertex join of $G_1$ and $G_2,$ denoted by $G_1 \star G_2.$ Let $S(G)$ be the subdivision graph of $G.$ The $SSG$-vertex join $G_1\star G_2$ is the graph obtained from $S(G_1)$ and $S(G_2)$ by joining each vertex of $G_1$ with each vertex of $G_2.$ In this paper, when $G_i (i = 1, 2)$ is a regular graph, we determine the normalized Laplacian spectrum of $G_1 \star G_2.$ As applications, we construct many pairs of normalized Laplacian cospectral graphs, the normalized Laplacian energy, and the degree Kirchhoff index of $G_1 \star G_2.$

}, issn = {}, doi = {https://doi.org/2018-AAM-20588}, url = {https://global-sci.com/article/72732/on-the-normalized-laplacian-spectrum-of-a-new-join-of-two-graphs} }