@article{Santhakumaran_Athisayanathan_2017, title={The forcing connected detour number of a graph}, volume={33}, url={https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1284}, DOI={10.4067/S0716-09172014000200002}, abstractNote={<em style="font-size: small; text-align: justify;">For two vertices u and v in a graph G</em><span style="font-size: small; text-align: justify;"> = (V, E), </span><em style="font-size: small; text-align: justify;">the detour distance D(u,</em><span style="font-size: small; text-align: justify;"> v) </span><em style="font-size: small; text-align: justify;">is the length of a longest u—v path in G.A u—v path of length D(u,</em><span style="font-size: small; text-align: justify;"> v) </span><em style="font-size: small; text-align: justify;">is called a u—v detour. A set ⊆ </em><span style="font-size: small; text-align: justify;">V </span><em style="font-size: small; text-align: justify;">is called a detour set of G if every vertex in G lies on a detour joining a pair of vertices of S.The detour number dn(G) of G is the minimum order of its detour sets and any detour set of order dn(G) is a detour basis of G.A set ⊆</em><span style="font-size: small; text-align: justify;"> V </span><em style="font-size: small; text-align: justify;">is called a connected detour set of G if S is detour set of G and the subgraph</em><span style="font-size: small; text-align: justify;"> G[S] </span><em style="font-size: small; text-align: justify;">induced by S is connected. The connected detour number cdn(G) of G is the minimum order of its connected detour sets and any connected detour set of order cdn(G) is called a connected detour basis of G.A subset T of a connected detour basis S is called a forcing subset for S if S is theuniquecon-nected detour basis containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing connected detour number of S, denoted by fcdn(S), is the cardinality of a minimum forcing subset for S. The forcing connected detour number of G, denoted by fcdn(G),is fcdn(G) = min{fcdn(S)},where the minimum is taken over all connected detour bases S in G. The forcing connected detour numbers ofcertain standard graphs are obtained. It is shown that for each pair a, b of integers with</em><span style="font-size: small; text-align: justify;"> 0 ≤ </span><em style="font-size: small; text-align: justify;">a < b and b</em><span style="font-size: small; text-align: justify;"> ≥ 3, </span><em style="font-size: small; text-align: justify;">there is a connected graph G with fcdn(G) = a and cdn(G) = b.</em>}, number={2}, journal={Proyecciones (Antofagasta, On line)}, author={Santhakumaran, A. P. and Athisayanathan, S.}, year={2017}, month={Mar.}, pages={147-155} }