TY - JOUR
ID - 1588
TI - The order difference interval graph of a group
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Balakrishnan, P.
AU - Kala, R.
AD - Department of Mathematics,
Manonmaniam Sundaranar University, tirunelveli
AD - Department of Mathematics
Manonmaniam Sundaranar University
Tirunelveli 627 012, Tamil Nadu, India.
Y1 - 2012
PY - 2012
VL - 1
IS - 2
SP - 59
EP - 65
KW - Order difference interval graph
KW - unicyclic graph
KW - Eulerian
KW - gen-
erating set
DO - 10.22108/toc.2012.1588
N2 - In this paper we introduce the concept of order difference interval graph $\Gamma_{ODI}(G)$ of a group $G$. It is a graph $\Gamma_{ODI}(G)$ with $V(\Gamma_{ODI}(G)) = G$ and two vertices $a$ and $b$ are adjacent in $\Gamma_{ODI}(G)$ if and only if $o(b)-o(a) \in [o(a), o(b)]$. Without loss of generality, we assume that $o(a) \leq o(b)$. In this paper we obtain several properties of $\Gamma_{ODI}(G)$, upper bounds on the number of edges of $\Gamma_{ODI}(G)$ and determine those groups whose order difference interval graph is isomorphic to a complete multipartite graph.
UR - https://toc.ui.ac.ir/article_1588.html
L1 - https://toc.ui.ac.ir/article_1588_9fb8176991b10ac13f1c1c7d632dd893.pdf
ER -