TY  - JOUR
ID  - Nikandish2017
LB  - Nikandish2017
AU  - Nikandish, Reza
AU  - Shaveisi, Farzad
TI  - On the structure of compact graphs
ST  - On the structure of compact graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 6
SP  - 875
EP  - 886
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.6.875
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.6.875
AB  - A simple graph \(G\) is called a compact graph if \(G\) contains no isolated vertices and for each pair \(x\), \(y\) of non-adjacent vertices of \(G\), there is a vertex \(z\) with \(N(x)\cup N(y)\subseteq N(z)\), where \(N(v)\) is the neighborhood of \(v\), for every vertex \(v\) of \(G\). In this paper, compact graphs with sufficient number of edges are studied. Also, it is proved that every regular compact graph is strongly regular. Some results about cycles in compact graphs are proved, too. Among other results, it is proved that if the ascending chain condition holds for the set of neighbors of a compact graph \(G\), then the descending chain condition holds for the set of neighbors of \(G\).
KW  - compact graph
KW  - vertex degree
KW  - cycle
KW  - neighborhood
SN  - 1232-9274
ER  -