Opuscula Math. 37, no. 6 (2017), 875-886
http://dx.doi.org/10.7494/OpMath.2017.37.6.875

Opuscula Mathematica

# On the structure of compact graphs

Reza Nikandish

Abstract. 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 $$G$$.

Keywords: compact graph, vertex degree, cycle, neighborhood.

Mathematics Subject Classification: 05C07, 05C38, 68R10.

Full text (pdf)

Reza Nikandish, Farzad Shaveisi, On the structure of compact graphs, Opuscula Math. 37, no. 6 (2017), 875-886, http://dx.doi.org/10.7494/OpMath.2017.37.6.875

a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.