Browsing by Author "LHR TP 7626"

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    Secure Resolving Dimension of Zero Divisor Graphs Associated to Commutative Rings
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Muzammil; CIIT/SP20-RMT-012/LHR; Dr. Hafiz Muhammad Afzal Siddiqui; LHR TP 7626
    This Thesis contains the study of secure resolving dimensions of certain zero divisor graphs of commutative ring with unity. A subset 𝑇 of 𝐺 is a secure resolving set for 𝐺 if 𝑇 is resolving and for any 𝑥 ∈ 𝑉 − 𝑇, there exists 𝑦 ∈ 𝑇 such that (𝑇 − {𝑦}) ∪ {𝑥} is a resolving set for 𝐺. The minimum cardinality of a secure resolving set for 𝐺 is known as the secure resolving dimension for 𝐺. We determine the secure resolving dimension of various zero divisor graphs derived from commutative ring with unity and prove that all these graphs have constant secure resolving dimension