Restrained reinforcement number in graphs

A set $S$ of vertices is a restrained dominating set of a graph $G=(V,E)$ if every vertex in $V\setminus S$ has a neighbor in $S$ and a neighbor in $V\setminus S$. The minimum cardinality of a restrained dominating set is the restrained domination number $\gamma_{r}(G)$. In this paper we initiate the study of the restrained reinforcement number $r_{r}(G)$ of a graph $G$ defined as the cardinality of a smallest set of edges $F\subseteq E(\overline{G})$ for which $\gamma _{r}(G+F

Dynamic programming for graphs on surfaces

We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic programming runs in 2O(k·log k). Our approach combines tools from topological graph theory and analytic combinatorics.Postprint (updated version

Bounds on several versions of restrained domination number

We investigate several versions of restraineddomination numbers and present new bounds on these parameters. We generalize theconcept of restrained domination and improve some well-known bounds in the literature.In particular, for a graph $G$ of order $n$ and minimum degree $\delta\geq 3$, we prove thatthe restrained double domination number of $G$ is at most $n-\delta+1$. In addition,for a connected cubic graph $G$ of order $n$ we show thatthe total restrained domination number of $G$ is at least $n/3$ andthe restrained double domination number of $G$ is at least $n/2$

Fair Restrained Dominating Set in the Corona of Graphs

In this paper, we give the characterization of a fair restrained dominating set in the corona of two nontrivial connected graphs and give some important results