Vertex Triangle Free Detour Number of a Graph

Authors

  • S Sethu Ramalingam St. Xavier's College (Autonomous), Palayamkottai
  • I Keerthi Asir St. Xavier's College (Autonomous), Palayamkottai
  • S Athisayanathan, Ph D St. Xavier's College (Autonomous), Palayamkottai

DOI:

https://doi.org/10.12723/mjs.38.2

Abstract

The \emph{$x$-triangle free detour number} $dn_{\triangle f_x}(G)$ of a connected graph $G$ is the minimum order of its $x$-triangle free detour sets and any $x$-triangle free detour set $S_{x} \subseteq V$ of orderĀ  $dn_{\triangle f_x}(G)$ is a \emph{$x$-triangle free detour basis} of $G$. A connected graph of order $n$ with vertex triangle free detour number $n-1$ or $n-2$ for every vertex is characterized. Certain general properties satisfied by the vertex triangle free detour sets are studied.

Author Biographies

S Sethu Ramalingam, St. Xavier's College (Autonomous), Palayamkottai

St. Xavier's College (Autonomous), Palayamkottai 627002

I Keerthi Asir, St. Xavier's College (Autonomous), Palayamkottai

St. Xavier's College(Autonomous), Palayamkottai 627002

S Athisayanathan, Ph D, St. Xavier's College (Autonomous), Palayamkottai

St. Xavier's College (Autonomous), Palayamkottai 627002

Additional Files

Published

2021-08-28