Outer-convex Domination in the Composition and Cartesian Product of Graphs

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Jonecis Adolfo Dayap
Enrico Limbo Enriquez

Abstract

Let G be a connected simple graph. A set S of vertices of a graph G is an outer-convex dominating set if every vertex not in S is adjacent to some vertex in S and V (G) \ S is a convex set. In this paper we characterize the outer-convex dominating sets in the composition and Cartesian product of two connected graphs. It is shown that the outer-convex domination number of a composition G[H] of two connected graphs G = Pm (m ≥ 3) and H = Kn (n ≥ 2) is equal to 2 if m = 3 and n(m − 4) + 2 if m > 3. The outer-convex domination number of the Cartesian product G□H of two non-complete connected graphs G and H depends on the outer-convex domination number of G and H.

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How to Cite
Dayap, J. A., & Enriquez, E. L. (2019). Outer-convex Domination in the Composition and Cartesian Product of Graphs. Journal of Global Research in Mathematical Archives(JGRMA), 6(3), 34–42. Retrieved from https://jgrma.com/index.php/jgrma/article/view/526
Section
Research Paper
Author Biographies

Jonecis Adolfo Dayap, University of San Jose-Recoletos

Instructor in Department of Mathematics and Sciences, University of San Jose-Recoletos

Enrico Limbo Enriquez, University of San Carlos

Professor in Department of Mathematics, University of San Carlos

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