Geodesic
Further Results on the Outer Connected Geodetic Number of a Graph
Publications de l'Institut Mathématique, _N_S_108 (2020) no. 122, p. 79

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DOI

For a connected graph $G$ of order at least two, an outer connected geodetic set $S$ in a connected graph $G$ is called a \emph{minimal outer connected geodetic set} if no proper subset of $S$ is an outer connected geodetic set of $G$. The \emph{upper outer connected geodetic number} $g_{\operatorname{oc}}^{+}(G)$ of $G$ is the maximum cardinality of a minimal outer connected geodetic set of $G$. We determine bounds for it and find the upper outer connected geodetic number of some standard graphs. Some realization results on the upper outer connected geodetic number of a graph are studied. The proposed method can be extended to the identification of beacon vertices towards the network fault-tolerant in wireless local access network communication. Also, another parameter \emph{forcing outer connected geodetic number} $f_{\operatorname{og}}(G)$ of a graph $G$ is introduced and several interesting results and realization theorem are proved.
DOI : 10.2298/PIM2022079G
Classification : 05C12
Keywords: geodetic set, outer connected geodetic set, outer connected geodetic number, upper outer connected geodetic set, forcing outer connected geodetic number 
Kathiresan Ganesamoorthy; Duraisamy Jayanthi. Further Results on the Outer Connected Geodetic Number of a Graph. Publications de l'Institut Mathématique, _N_S_108 (2020) no. 122, p. 79 . doi: 10.2298/PIM2022079G
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     journal = {Publications de l'Institut Math\'ematique},
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