Independent-[1, 2] sets of the subdivision graph, middle graph and R-graph of some families of graphs

Date of Publication

2026

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with Specialization in Computer Applications

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Advisor

Francis Joseph H. Campena

Defense Panel Chair

Michele G. Tan

Defense Panel Member

Isagani B. Jos

Abstract (English)

A subset 𝑆 βŠ† 𝑉 is an independent [1, 2]-set of the graph 𝐺 if 𝑆 is an independent dominating set and for every 𝑣 ∈ 𝑉 βˆ– 𝑆, 1 ≀ |𝑁 (𝑣) ∩ 𝑆| ≀ 2. This means that each vertex outside 𝑆 is adjacent to at least 1 and at most 2 elements of 𝑆 and that any two vertices in 𝑆 do not have an edge in 𝐺. In this work, we are interested in determining if the graph obtained by some operations; such as the subdivision graph, 𝑅-graph, and the middle graph, has an independent [1, 2]-set.

Abstract Format

html

Abstract (Filipino)

Ang isang subset S βŠ† V ay isang independent [1, 2]-set ng graph G kung ang S ay isang independent dominating set at para sa bawat v ∈ V \ S, 1 ≀ |N (v) ∩ S| ≀ 2. Nangangahulugan ito na bawat vertex na nasa labas ng S ay adjacent ng hindi bababa sa 1 at hindi hihigit sa 2 element ng S at ang anumang dalawang vertex sa S ay walang edge sa G. Sa papel na ito, interesado kaming matukoy kung ang graph na nakuha sa ilang operations; tulad ng subdivision graph, R-graph, at middle graph, ay may independent [1, 2]-set.

Abstract Format

html

Language

English

Format

Electronic

Keywords

Graph theory

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Embargo Period

4-15-2026

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