Investigating Weakly Connected 2-Domination in the Complementary Prism of Graphs and in Some Unary Graph Operations

Mae P. Militante; Doli-Jane U. Tejada; Nadjua E. Seddic; Francis Nixon D. Demata; Emmanuel Campos

doi:10.26713/cma.v16i1.2837

Authors

Mae P. Militante Department of Mathematics, Mindanao State University – General Santos, General Santos City, Philippines https://orcid.org/0000-0002-5632-0340 (unauthenticated)
Doli-Jane U. Tejada Department of Mathematics, Mindanao State University – General Santos, General Santos City, Philippines https://orcid.org/0009-0008-9780-6786 (unauthenticated)
Nadjua E. Seddic Department of Mathematics, Mindanao State University – General Santos, General Santos City, Philippines https://orcid.org/0009-0005-9185-5972 (unauthenticated)
Francis Nixon D. Demata Department of Mathematics, Mindanao State University – General Santos, General Santos City, Philippines https://orcid.org/0009-0001-1508-9736 (unauthenticated)
Emmanuel Campos Department of Mathematics, Mindanao State University – General Santos, General Santos City, Philippines https://orcid.org/0009-0005-7755-1075 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v16i1.2837

Keywords:

Weakly connected 2-domination, Complementary prism, Edge deletion, Vertex deletion, Unary operations, Line graphs

Abstract

This paper dealt with the concepts of weakly connected 2-domination in the complementary prisms of graphs and graphs obtained by reducing their edges and vertices. In particular, bounds and exact values of the weakly connected 2-domination number in the complementary prism of graphs, graphs resulting from deleting an edge and vertex and line graphs are presented. In addition, properties of the graphs with weakly connected 2-domination number of complementary prism equal to 2 and 3, are provided.

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