Applied Mathematical Sciences, Vol. 8, 2014, no. 98, 4867 - 4875 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.46396 Forcing Weakly Convexity Number of a Graph Kezza P. Noguerra 1 Department of Mathematics and Statistics Mindanao State University-Iligan Institute of Technology Tibanga Highway, Iligan City, Philippines Sergio R. Canoy, Jr., Helen M. Rara and Elgie T. Liwagon Department of Mathematics and Statistics Mindanao State University-Iligan Institute of Technology Tibanga Highway, Iligan City, Philippines Copyright c  2014 Kezza P. Noguerra, Sergio R. Canoy, Jr, Helen M. Rara and Elgie T. Liwagon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we introduce the concepts of forcing weakly convexity and forcing weakly convexity number of a graph. We also determine the forcing weakly convexity numbers of some special graphs and graphs under some binary operation such as the join, corona and composition of two graphs. Mathematics Subject Classification: 05C12 Keywords: weakly convex set, forcing weakly convex subset, weakly con- vexity number, forcing weakly convexity number 1 Introduction Let G =(V (G),E(G)) be a simple connected graph. Let u, v ∈ V (G). Then the distance d G (u, v) between u and v, is the length of the shortest u-v path in G.A u-v path of length d G (u, v) is called u-v geodesic. The diameter diam(G) 1 This research is partially funded by DOST-ASTHRDP.