@article{Santhakumaran_Mahendran_2017, title={The forcing open monophonic number of a graph}, volume={35}, url={https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1235}, DOI={10.4067/S0716-09172016000100005}, abstractNote={<span style="font-family: verdana; font-size: small; text-align: justify;">For a connected graph G of order n ≥ 2, and for any mínimum open monophonic set S of G, a subset T of S is called a forcing subset for S if S is the unique minimum open monophonic set containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing open monophonic number of S, de-noted by f</span><sub style="font-family: verdana; text-align: justify;">om</sub><span style="font-family: verdana; font-size: small; text-align: justify;">(S), is the cardinality of a minimum forcing subset of S. The forcing open monophonic number of G, denoted by f</span><sub style="font-family: verdana; text-align: justify;">om</sub><span style="font-family: verdana; font-size: small; text-align: justify;">(G), is f</span><sub style="font-family: verdana; text-align: justify;">om</sub><span style="font-family: verdana; font-size: small; text-align: justify;">(G) = min(f</span><sub style="font-family: verdana; text-align: justify;">om</sub><span style="font-family: verdana; font-size: small; text-align: justify;">(S)), where the minimum is taken over all minimum open monophonic sets in G. The forcing open monophonic numbers of certain standard graphs are determined. It is proved that for every pair a, b of integers with 0 ≤ a ≤ b — 4 and b ≥ 5, there exists a connected graph G such that f</span><sub style="font-family: verdana; text-align: justify;">om</sub><span style="font-family: verdana; font-size: small; text-align: justify;">(G) = a and om(G) = b. It is analyzed how the addition of a pendant edge to certain standard graphs affects the forcing open monophonic number.</span>}, number={1}, journal={Proyecciones (Antofagasta, On line)}, author={Santhakumaran, A. P. and Mahendran, M.}, year={2017}, month={Mar.}, pages={67-83} }