[PDF] Top 20 Connectivity problems on heterogeneous graphs

... network connectivity prob- lems that are commonly used in PPI analysis—such as Shortest Path, Steiner Tree, Prize-Collecting Steiner Tree— when conditions are ...these problems, we cannot guarantee (in ... See full document

... related problems on supergrid graphs can be applied to control the stitching trace of a computerized sewing machine as stated in ...grid graphs is ...grid graphs are not Hamiltonian ...grid ... See full document

... of graphs were understood and explored well in the literature while there is insufficient research related to directed ...many problems to be solved with respect to ...2-vertex connectivity is an ... See full document

... many problems of real life where we deal with two essential but opposite attributes of a ...basic connectivity concepts like strength of connectedness into bipolar fuzzy graphs and also introduced ... See full document

... connected problems on grid, triangular grid, and supergrid graphs have received much ...grid graphs is ...grid graphs are not Hamiltonian ...grid graphs of positive width have ... See full document

... intersection graphs, we cannot determine the starting position of an algorithm uniquely for a circular intersection graph owing to the existence of feedback ...several problems, we can develop circular ... See full document

... cycle problems have numerous applications in different areas, including establishing transport routes, production launching, the on- line optimization of flexible manufacturing systems [1], com- puting the ... See full document

... A graph is a more suitable way of representing informa- tion involving relationship between objects. The objects are represented by vertices and relations by edges. The graph theoretical models are used to represent ... See full document

... the connectivity of a k-colour graph have applications in re- assignment problems of the channels used in cellular networks; see, ...These problems can be expressed in finding paths in strong ... See full document

... graph problems. Here, we have presented new connectivity concepts in intuitionistic fuzzy labeling ...by connectivity concepts of intuitionistic fuzzy ...fuzzy graphs, (2) Chromatic number in ... See full document

... Intersection graphs introduced by Pal [9] also exhibit an important relation between communication system and graph ...theory. Connectivity is one main concept underlying applications of weighted ... See full document

... for heterogeneous wireless sensor networks is ...and heterogeneous sensor nodes that have greater power and transmission capability than other nodes ...the connectivity of wireless sensor networks ... See full document

... Let G be a graph on n vertices. We denote the vertex and the edge set of G by V(G) and E(G), respectively. For two vertices u and v of V(G) we define their distance d(u,v) as the length of any shortest path connecting u ... See full document

... Topological indices are useful tools for theoretical chemistry. A structural formula of a chemical compound is represented by a molecular graph. The atoms of the compounds and chemical bonds represent the vertices and ... See full document

... As an immediate application of Lemma , we know that the complete graph is the unique graph with maximum ABC index among connected graphs. Furthermore, we can deduce that the upper bound of ABC(G) – r(G) would be ... See full document

... It was named as, “ branching index" by Randi´c himself. Soon after it was re-named as, “connectivity index" [18] and [19]. Now it is referred as, “Randi´c index". It is most often applied and most ... See full document

... eccentric connectivity index [2-6]  C ( ) x of a graph G is defined as  C ( ) x   u V G  ( ) deg( ) ( ) u  u , where deg(u) denotes the degree of vertex u in G, ...eccentric connectivity index and ... See full document

... First we recall some notations. We denote by κ (G) and δ(G) the edge connectivity and the minimum degree of a graph G, respectively. Let S be a nonempty proper subset of V . We use G[S] to denote the subgraph of G ... See full document

... Molecular graphs are significantly important in showing the mathematic applications in ...finite graphs then a topological index is a function Top from Λ into real numbers with ... See full document

... eccentric connectivity index of TUC C (s) 4 8 nanotube and TC C (s) ...eccentric connectivity index of chemical ...eccentric connectivity index of ...eccentric connectivity index of unicyclic ... See full document