A geodetic set $S$ in a graph $G$ is called a total restrained geodetic set if the induced subgraphs $G[S]$ and $G[V-S]$ have no isolated vertex. The minimum cardinality of a total restrained geodetic set in $G$ is the total restrained geodetic number and is denoted by $g_{tr} (G)$. In this paper we initiate the study of the total restrained geodetic number in graphs. We first characterize all connected graphs with no extreme vertex and large total restrained geodetic number, and then we present some realizable results.
Abdollahzadeh Ahangar, H. and Najimi, M. (2016). Total restrained geodetic number of graphs. Iranian Journal of Science, (), -. doi: 10.22099/ijsts.2016.3572
MLA
Abdollahzadeh Ahangar, H. , and Najimi, M. . "Total restrained geodetic number of graphs", Iranian Journal of Science, , , 2016, -. doi: 10.22099/ijsts.2016.3572
HARVARD
Abdollahzadeh Ahangar, H., Najimi, M. (2016). 'Total restrained geodetic number of graphs', Iranian Journal of Science, (), pp. -. doi: 10.22099/ijsts.2016.3572
CHICAGO
H. Abdollahzadeh Ahangar and M. Najimi, "Total restrained geodetic number of graphs," Iranian Journal of Science, (2016): -, doi: 10.22099/ijsts.2016.3572
VANCOUVER
Abdollahzadeh Ahangar, H., Najimi, M. Total restrained geodetic number of graphs. Iranian Journal of Science, 2016; (): -. doi: 10.22099/ijsts.2016.3572
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