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VERTEX COVERING TRANSVERSAL GEODOMATIC NUMBER OF A GRAPH
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A geodetic set S ⊆ V in a simple graph G = (V, E), which intersects every minimum vertex covering set (α0-set), is called a vertex covering transversal geodetic set [7]. The minimum cardinality of a vertex covering transversal geodetic set of G is called the vertex covering transversal geodetic number of G and is denoted by gvct(G) [7]. A partition (S1, S2, ..., Sk) of V is called a vertex covering transversal geodomatic partition of G if each Si is a vertex covering transversal geodetic set in G. The maximum cardinality of a vertex covering transversal geodomatic partition of G is called the vertex covering transversal geodomatic number of G and is denoted by dgvct (G). In this paper, we investigate the parameter known as the vertex covering transversal geodomatic number for different types of graphs and examine its structural properties.
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Title: VERTEX COVERING TRANSVERSAL GEODOMATIC NUMBER OF A GRAPH
Description:
A geodetic set S ⊆ V in a simple graph G = (V, E), which intersects every minimum vertex covering set (α0-set), is called a vertex covering transversal geodetic set [7].
The minimum cardinality of a vertex covering transversal geodetic set of G is called the vertex covering transversal geodetic number of G and is denoted by gvct(G) [7].
A partition (S1, S2, .
, Sk) of V is called a vertex covering transversal geodomatic partition of G if each Si is a vertex covering transversal geodetic set in G.
The maximum cardinality of a vertex covering transversal geodomatic partition of G is called the vertex covering transversal geodomatic number of G and is denoted by dgvct (G).
In this paper, we investigate the parameter known as the vertex covering transversal geodomatic number for different types of graphs and examine its structural properties.
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