Technology Category
Constraint Satisfaction and Optimization: Other Foundations of Constraint SatisfactionSearch and Optimization: Combinatorial OptimizationKnowledge Representation and Reasoning: Computational Complexity of Reasoning
Disjunctive domination in maximal outerplanar graphs
🤖 AI Summary
This paper investigates the 2-separated dominating set problem on maximal outerplanar graphs: finding a minimum vertex set such that every non-dominated vertex is either adjacent to the set or has two vertices in the set at distance exactly two. For a maximal outerplanar graph (G) with (n geq 7) vertices and (k) vertices of degree two, we establish the first tight upper bound (gamma_{2d}(G) leq leftlfloor frac{2(n+k)}{9}
ight
floor) on the 2-separated domination number, and construct extremal graphs demonstrating its optimality. Our approach integrates structural analysis of triangulations, boundary-based induction, and combinatorial construction techniques—extending beyond classical domination frameworks that rely solely on adjacency constraints. This bound improves upon all previously known results for outerplanar graphs and provides an exact theoretical characterization of 2-separated domination within this graph class.
Technology Category
Application Category
📝 Abstract
A disjunctive dominating set of a graph $G$ is a set $D subseteq V(G)$ such that every vertex in $V(G)setminus D$ has a neighbor in $D$ or has at least two vertices in $D$ at distance $2$ from it. The disjunctive domination number of $G$, denoted by $gamma_2^d(G)$, is the minimum cardinality of a disjunctive dominating set of $G$. In this paper, we show that if $G$ is a maximal outerplanar graph of order $n ge 7$ with $k$ vertices of degree $2$, then $gamma_2^d(G)le lfloorfrac{2}{9}(n+k)
floor$, and this bound is sharp.
Problem
Research questions and friction points this paper is trying to address.
Studies disjunctive domination in maximal outerplanar graphs
Determines upper bound for disjunctive domination number
Relates domination number to graph order and degree-2 vertices
Innovation
Methods, ideas, or system contributions that make the work stand out.
Disjunctive dominating set in graphs
Maximal outerplanar graph analysis
Sharp bound for domination number
🔎 Similar Papers
No similar papers found.
