eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences April, 2017 29 4 183 191 http://dx.doi.org/10.22147/jusps-A/290408 793 article RANDY L. CAGA-ANAN (randy.caga-anan@g.msuiit.edu.ph) 1 Department of Mathematics and Statistics College of Science and Mathematics Mindanao State University-Iligan Institute of Technology Iligan City 9200, Philippines <p style="text-align:justify">Let G = (V (G), E(G)) be an undirected connected graph and let X be a subset of V (G) . Furthermore, let I (X ) and B(X ) denote the set of isolates and the boundary set of X, respectively. The inner boundary number of X, denoted by (X ) i is (X) = max{|Y |:Y X and B(X Y) Y = B(X)}. i   The outer boundary number of X, denoted by (X ) o  is (X ) =|V(G) N[X ]| . o  The I -integral of X is I  (X ) = (X ) (X ) | I(X ) | i o     and the I -integral of G is I  (G) = min{ I  (X ) : X V(G)}I&nbsp;. In this paper, we determine the I -integral of graphs resulting from some binary operations such as the join, corona, composition, and cartesian product of graphs.</p> https://www.ultrascientist.org/paper/793/ I -integral isolates boundary Mathematics Subject Classification: 05C69