Vertex semi-middle graph of a graph
Rajendra Prasad K C, K. M. Niranjan, Venkanagouda M Goudar · Malaya Journal of Matematik · 2019
In this communication, the vertex semi-middle graph of a graph $M_v(G)$ is introduced. We obtain a characterization of graphs whose $M_v(G)$ is planar, outerplanar and minimally non-outerplanar. Further, we obtain $M_v(G)$ is Eulerian, crossing number one and crossing number two.