Abstract

The Forcing Open Geodetic Domination Number of a Graph

V. Vijimon Moni*1 and S. Robinson Chellathurai2

*1Research Scholar, Department of Mathematics, Scott Christian College, Nagercoil-629 003, Tamil Nadu, INDIA. 2Associate Professor, Department of Mathematics, Scott Christian College, Nagercoil-629 003, Tamil Nadu, INDIA. email:*1vijimon1983@gmail.com, 2robinchel@rediffmail.com Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627 012, Tamil Nadu, INDIA.

DOI : http://dx.doi.org/10.29055/jcms/1130

ABSTRACT

Let 𝐺 be a connected graph with at least two vertices and 𝑆 a minimum open geodetic dominating set of 𝐺. A subset 𝑇 of 𝑆 is called a forcing subset for 𝑆 if 𝑆 is the unique minimum open geodetic dominating set containing 𝑇. A forcing subset for 𝑆 of minimum cardinality is a minimum forcing subset of 𝑆. The forcing open geodetic dominating number of 𝑆, denoted by π‘“π›Ύπ‘œπ‘”(𝑆), is the cardinality of a minimum forcing subset of 𝑆. The forcing open geodetic dominating set of 𝐺 denoted by π‘“π›Ύπ‘œπ‘”(𝐺) is π‘“π›Ύπ‘œπ‘”(𝐺) = min{π‘“π›Ύπ‘œπ‘”(𝑆)}, where the minimum is taken over all minimum forcing open geodetic dominating sets in 𝐺. Some general properties satisfied by this concept are studied. For every pair π‘Ž,𝑏 of integers with 0 ≀ π‘Ž< 𝑏 and 𝑏 β‰₯ 6, there exists a connected graph G such that π‘“π›Ύπ‘œπ‘”(G) = π‘Ž and π›Ύπ‘œπ‘”(𝐺) = b. AMS Subject Classification: 05C12.

Keywords :open geodetic dominating number, forcing open geodetic dominating number.

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