Open AccessГраф блоков
Author(s) -
A. Kelkar,
K. Jaysurya,
H.M. Nagesh
Publication year - 2019
Publication title -
vladikavkazskij matematičeskij žurnal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.126
H-Index - 2
eISSN - 1814-0807
pISSN - 1683-3414
DOI - 10.23671/vnc.2019.1.27736
Subject(s) - combinatorics , outerplanar graph , mathematics , eulerian path , vertex (graph theory) , planar graph , graph , planar , discrete mathematics , pathwidth , line graph , computer science , lagrangian , pure mathematics , computer graphics (images)
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.