• ON THE FORCING HULL AND FORCING GEODETIC NUMBERS OF GRAPHS
Abstract
In this paper, we prove that, for any non-negative integers a, b, c and d with a < c < d, b < d, c > a + 1 and
d > b + c – a , there exists a connected graph G such that fh(G) = a , fg(G) = b, h(G) = c and g(G) = d, where fh(G) , fg(G) , h(G) and g(G) are the forcing hull number, the forcing geodetic number, the hull number and the geodetic number of a graph respectively. This result solves a problem of Li-Da Tong [Li-Da Tong, The forcing hull and forcing geodetic numbers of graphs, Discrete Applied Mathematics, 157 (2009), 1159-1163]
d > b + c – a , there exists a connected graph G such that fh(G) = a , fg(G) = b, h(G) = c and g(G) = d, where fh(G) , fg(G) , h(G) and g(G) are the forcing hull number, the forcing geodetic number, the hull number and the geodetic number of a graph respectively. This result solves a problem of Li-Da Tong [Li-Da Tong, The forcing hull and forcing geodetic numbers of graphs, Discrete Applied Mathematics, 157 (2009), 1159-1163]
Keywords
hull number, geodetic number, forcing hull number, forcing geodetic number.
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