International Journal of Advances in Mathematics
International Journal of Advances in Mathematics
2456-6098
Volume 2018
Number 4
2018
July
02
Hangable graphs
44
50
EN
Mateusz
Miotk
Faculty of Mathematics, Physics and Informatics, University of Gda$\acute{n}$sk, 80-952 Gda$\acute{n}$sk, Poland.
j.topp@inf.ug.edu.pl
Jerzy Topp
Topp
The State University of Applied Sciences in Elblag, 82-300 Elblag, Poland.
j.topp@inf.ug.edu.pl
The distance
$d_G(u,v)$ between vertices $u$ and $v$ in $G$ is the length of a shortest $u-v$ path
in $G$. The eccentricity of a vertex $v$ in $G$ is the integer $e_G(v)= \max\{ d_G(v,u)
\colon u\in V_G\}$. The diameter of $G$ is the integer $d(G)= \max\{e_G(v)\colon
v\in V_G\}$. The periphery of a~vertex $v$ of $G$ is the set $P_G(v)= \{u\in V_G\colon
d_G(v,u)= e_G(v)\}$, while the periphery of $G$ is the set $P(G)= \{v\in V_G\colon
e_G(v)=d(G)\}$. A graph $G$ is said to be hangable if $P_G(v)\subseteq
P(G)$ for every vertex $v$ of $G$. In this paper we prove that every block
graph is hangable and discuss the hangability of products of graphs.
Hangability; Diameter; Block graph.
http://adv-math.com/hangable-graphs/
http://adv-math.com/wp-content/uploads/2018/07/ADV-201813-Hangable-graphs.pdf