[PDF] Top 20 Eternal Independent Sets in Graphs

... Well-covered graphs (i.e., graphs in which all maximal independent sets have the same cardinality) have this property, since there exists a perfect matching between the vertices in the ... See full document

... dominating sets in graph was introduced by Ore and Berge in ...fuzzy graphs and obtain several bounds for the domination ...fuzzy graphs using strong edges was discussed by Nagoorgani and ... See full document

... those graphs achieving the largest number was proposed by Erdös and Moser, and solved by Moon and Moser ...of graphs in the literature, including trees, forests, (connected) graphs with at most one ... See full document

... being independent transversal paired domination instead of domination alone or any other type of domination and call this partition an independent transversal paired domatic ...an independent ... See full document

... for graphs have been studied by several authors [5, ...stable sets and edge independent sets for ...maximal sets of the above ... See full document

... maximum independent set problem restricted to the class of line ...arbitrary graphs. Clearly, for general graphs these tools do not provide efficient ...for graphs with particular properties ... See full document

... We remark that Lemma 2.4 was already essentially proven in [8] (without applying Lemma 2.3). Note that γ could be negative in Lemma 2.4. The upper bound 1/11 on γ here can be relaxed to any constant smaller than 1/10 ... See full document

... two independent edges between 𝑃𝑃 𝑖𝑖 and 𝑃𝑃 𝑗𝑗 , say 𝑒𝑒 𝑖𝑖 ′ 𝑒𝑒 𝑗𝑗 ′ , 𝑒𝑒 𝑖𝑖 " 𝑒𝑒 𝑗𝑗 " ∈ 𝐸𝐸, then �𝐷𝐷\�𝑥𝑥 𝑖𝑖 , 𝑥𝑥 𝑗𝑗 �� ∪ �𝑒𝑒 𝑖𝑖 ′ , 𝑒𝑒 𝑗𝑗 " � ≠ 𝐷𝐷 is a minimum dominating set of G, which is a ... See full document

... There is a further variant which we will call “implicit” vertex streams (as opposed to the normal explicit representation). In this model, the stream consists of a series of small (polylog(n)-sized) identifiers – one per ... See full document

... weight independent set (MWIS) problem, being NP-hard in general, admits a polynomial-time solution when restricted to the class of line ...line graphs to claw-free ...claw-free graphs to apple-free ... See full document

... An independent set is a subset S of V such that no two vertices in S are ...maximal independent set is an independent set that is not a proper subset of any other independent ...maximal ... See full document

... thistechnique of colouring we used the terminology sort of colouring and type of colouring. A sort of colouring is colouring expected not defined and need to be defined, also you can’t determine edges or vertices ... See full document

... Let G = (V, E) be a finite, simple and undirected graph with neither loops nor multiple edges. The order and size of G are denoted by n and m respec- tively. One of the fastest growing areas within graph theory is the ... See full document

... inclusive sets. We now introduce a new concept called 2-isolate inclusive sets in ...inclusive sets and maximal 2-isolate inclusive sets in ... See full document

... Harary et al [2] explained an interesting application in voting situations using the concept of domination. Hattingh and Renu [3] introduced on weak domination in graphs. Rosenfeld[7] introduced the notion of ... See full document

... Abstract. In this paper we introduce relatively prime dominating set of a graph G. Let G be a non–trivial graph. A set S ⊆ V is said to be relatively prime dominating set if it is a dominating set with at least two ... See full document

... interval graphs is discussed using the operations of Cartesian product, composition, union and ...interval graphs is constructed by applying the above operations on any two bipolar fuzzy interval ... See full document

... Cayley graphs and enumeration of Hamilton cycles and triangles can be found in Madhavi ...these graphs are studied by the authors [2] and the following results are required and they are presented without ... See full document

... SMCjournal Figure 10 : escribed circle opposite Theorem 8 The internal bisector of and the external bisectors of and are concurrent at a point , which is the centre of a circle which tou[r] ... See full document

... Conversely, if the four boys belong to the same group of friends hanging out together, the identification of the witness sets most likely fails in (18.a-b). That is probably the assumption done by (Ferreira, 2007) ... See full document