Document Type
Lecture
Publication Date
10-18-2023
Abstract
For a finite graph G, a vertex set D of G is said to be a dominating set of G, if every vertex v ∈ V(G) − D has a neighbor in D. Further, if D is an independent set of vertices (D is an independent set if there is no edge between any two vertices of D) as well, we say D is an independent dominating set. Define γi(G) to be the minimum cardinality among all independent dominating sets of G. The bondage number of G denoted by b(G), is defined as min{|B| : B ⊂ E(G) such that γ(G − B) > γ(G)}. Similarly, the independent bondage number of G denoted by bi(G) and is defined as min{|B| : B ⊂ E(G) such that γi(G−B) > γi(G)}. In 2022, PhamandWeiprovedthatbi(G) ≤ 9forplanargraphswithminimumdegree 3. We improve this upper bound by showing that bi(G) ≤ 8. In 2003, Fischermann et al. established upper bounds of bondage numbers for connected planar graphs based on girth (the length of a shortest cycle in the graph) conditions. However, to date, no upper bounds have been developed for the independent bondage number concerning connected planar graphs using girth conditions. In this talk, we also present upper bounds on independent bondage numbers for connected planar graphs utilizing girth conditions.
Relational Format
presentation
Recommended Citation
Gamladdalage, Kanchana, "The Independent Bondage Number of Planar Graphs with Degree Conditions and Girth Conditions" (2023). Combinatorics Seminar. 16.
https://egrove.olemiss.edu/math_combinatorics/16
