Independent Bondage Number in Planar Graphs Under Girth Constraints

E. G. K. M. Gamlath (), Andrew Pham and Bing Wei
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E. G. K. M. Gamlath: College of Health and Natural Sciences, Franklin Pierce University, Rindge, NH 03461, USA
Andrew Pham: Department of Physics, Chemistry, and Mathematics, Alabama A&M University, 4900 Meridian St N, Huntsville, AL 35811, USA
Bing Wei: Department of Mathematics, University of Mississippi, Oxford, MS 38677, USA

Mathematics, 2025, vol. 13, issue 22, 1-22

Abstract: Given a finite, simple, connected graph G with at least one edge, the independent bondage number b i ( G ) of G is the minimum size of an edge set, such that its deletion results in a graph with a strictly larger independent domination number than that of G . While the bondage number of graphs under girth constraints has been studied, very few results have yet been established for the independent bondage number. In this study, we establish upper bounds on the independent bondage number of planar graphs under given girth constraints, extending results on the bondage number by Fischermann, Rautenbach, and Volkmann and on the structures of planar graphs by Borodin and Ivanova. In particular, we identify additional structures and establish bounds on the independent bondage number for planar graphs with δ ( G ) ≥ 2 and g ( G ) ≥ 5 , δ ( G ) ≥ 3 and g ( G ) ≥ 4 , δ ( G ) ≥ 2 and g ( G ) ≥ 7 , and δ ( G ) ≥ 2 and g ( G ) ≥ 10 , showing that the corresponding bounds are b i ( G ) ≤ 5 , b i ( G ) ≤ 6 , b i ( G ) ≤ 4 , and b i ( G ) ≤ 3 , respectively.

Keywords: independent domination; independent bondage number; discharging method; structural properties of planar graphs; upper bounds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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