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яндекс.ћетрика

DOI: 10.23671/VNC.2019.1.27736

Block Graph of a Graph

Kelkar, A. , Jaysurya, K. , Nagesh, H. M.
Vladikavkaz Mathematical Journal 2019. Vol. 21. Issue 1.
Abstract:
The block graph of a graph \(G\), written \(B(G)\), is the graph whose vertices are the blocks of \(G\) and in which two vertices are adjacent whenever the corresponding blocks have a cut-vertex in common. We study the properties of \(B(G)\) and present the characterization of graphs whose \(B(G)\) are planar, outerplanar, maximal outerplanar, minimally non-outerplanar, Eulerian, and Hamiltonian. A necessary and sufficient condition for \(B(G)\) to have crossing number one is also presented.
Keywords: rossing number, inner vertex number, dutch windmill graph, complete graph.
Language: English Download the full text  
For citation: Kelkar, A., Jaysurya, K. and Nagesh, H. M. Block Graph of a Graph, Vladikavkaz Math. J., 2019, vol. 21, no. 1, pp. 74-78. DOI 10.23671/VNC.2019.1.27736
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