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Open AccessArticle

Signed Domination Number of the Directed Cylinder

1
Department of Mathematics, Shanghai University of Electric Power, Shanghai 200090, China
2
Department of Mathematics Education, Daegu Catholic University, Gyeongsan 38430, Korea
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1443; https://doi.org/10.3390/sym11121443
Received: 10 September 2019 / Revised: 17 November 2019 / Accepted: 19 November 2019 / Published: 23 November 2019
In a digraph D = ( V ( D ) , A ( D ) ) , a two-valued function f : V ( D ) { 1 , 1 } defined on the vertices of D is called a signed dominating function if f ( N [ v ] ) 1 for every v in D. The weight of a signed dominating function is f ( V ( D ) ) = v V ( D ) f ( v ) . The signed domination number γ s ( D ) is the minimum weight among all signed dominating functions of D. Let P m × C n be the Cartesian product of directed path P m and directed cycle C n . In this paper, the exact value of γ s ( P m × C n ) is determined for any positive integers m and n. View Full-Text
Keywords: signed domination number; signed dominating function; cartesian product; directed path; directed cycle signed domination number; signed dominating function; cartesian product; directed path; directed cycle
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Wang, H.; Kim, H.K. Signed Domination Number of the Directed Cylinder. Symmetry 2019, 11, 1443.

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