Characterization of classes of graphs with large general position number
Getting inspired by the famous no-three-in-line problem and by the general position subset selection problem from discrete geometry, the same is introduced into graph theory as follows. A set $S$ of vertices in a graph $G$ is a general position set if no element of $S$ lies on a geodesic between any...
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| creator | Thomas, Elias John V, Ullas Chandran S |
| description | Getting inspired by the famous no-three-in-line problem and by the general
position subset selection problem from discrete geometry, the same is
introduced into graph theory as follows. A set $S$ of vertices in a graph $G$
is a general position set if no element of $S$ lies on a geodesic between any
two other elements of $S$. The cardinality of a largest general position set is
the general position number ${\rm gp}(G)$ of $G.$ In \cite{ullas-2016} graphs
$G$ of order $n$ with ${\rm gp}(G)$ $\in \{2, n, n-1\}$ were characterized. In
this paper, we characterize the classes of all connected graphs of order $n\geq
4$ with the general position number $n-2.$ |
| doi_str_mv | 10.48550/arxiv.2004.04648 |
| format | Article |
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position subset selection problem from discrete geometry, the same is
introduced into graph theory as follows. A set $S$ of vertices in a graph $G$
is a general position set if no element of $S$ lies on a geodesic between any
two other elements of $S$. The cardinality of a largest general position set is
the general position number ${\rm gp}(G)$ of $G.$ In \cite{ullas-2016} graphs
$G$ of order $n$ with ${\rm gp}(G)$ $\in \{2, n, n-1\}$ were characterized. In
this paper, we characterize the classes of all connected graphs of order $n\geq
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position subset selection problem from discrete geometry, the same is
introduced into graph theory as follows. A set $S$ of vertices in a graph $G$
is a general position set if no element of $S$ lies on a geodesic between any
two other elements of $S$. The cardinality of a largest general position set is
the general position number ${\rm gp}(G)$ of $G.$ In \cite{ullas-2016} graphs
$G$ of order $n$ with ${\rm gp}(G)$ $\in \{2, n, n-1\}$ were characterized. In
this paper, we characterize the classes of all connected graphs of order $n\geq
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position subset selection problem from discrete geometry, the same is
introduced into graph theory as follows. A set $S$ of vertices in a graph $G$
is a general position set if no element of $S$ lies on a geodesic between any
two other elements of $S$. The cardinality of a largest general position set is
the general position number ${\rm gp}(G)$ of $G.$ In \cite{ullas-2016} graphs
$G$ of order $n$ with ${\rm gp}(G)$ $\in \{2, n, n-1\}$ were characterized. In
this paper, we characterize the classes of all connected graphs of order $n\geq
4$ with the general position number $n-2.$</abstract><doi>10.48550/arxiv.2004.04648</doi><oa>free_for_read</oa></addata></record> |
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| title | Characterization of classes of graphs with large general position number |
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