It is necessary to generate the automorphism group of a chemical graph in computer-aided structure elucidation. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce...

Given a tree and a set P of non-trivial simple paths on it, Vpt(P) is the VPT graph (i.e. the vertex intersection graph) of P, and Ept(P) is the EPT graph (i.e. the edge intersection graph) of the paths P of the tree T . These graphs have been extensively studied in the literature. Given two (edge) intersecting paths in a graph, their split vertices is the set of vertices having degree at least...

Splitting off a pair su; sv of edges in a graph G means the operation that deletes su and sv and adds a new edge uv. Given a graph G = (V + s;E) which is k-edge-connected (k 2) between vertices of V and a specified subset R V , first we consider the problem of finding a longest possible sequence of disjoint pairs (splittings) of edges sx; sy, x; y 2 R which can be split off preserving k-edge-co...

in this paper, we use the concept of graph convergence of h(.,.)-co-accretive mapping introduced by [r. ahmad, m. akram, m. dilshad, graph convergence for the h(.,.)-co-accretive mapping with an application, bull. malays. math. sci. soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...

Let G = (V, E) be a simple graph. A dominating set D is called a complementary tree dominating set if the induced subgraph is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number of G and is denoted by ctd(G). For a graph G, let V(G) = {v : v  V(G)} be a copy of V(G). The splitting graph Sp(G) of G is the graph with ...

a 1993 result of j. llibre, and m. misiurewicz, (theorem a [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. also a 1980 result of l.s. block, j. guckenheimer, m. misiurewicz and l.s. young (lemma 1.5 [3]) states that if g is an a-graph of f then h(g) ? h( f ). in this pap...

We present a graph coloring register allocator which uses an improved form of passive live range splitting to reduce the count of dynamic spill operations. Program structure is used to guide the global splitting of live ranges and to place split operations at infrequently executed portions of the program. We also optimistically reconsider spill decisions at certain points to potentially enable ...

Let G be the graph of a triangulated surface Σ of genus g ≥ 2. A cycle of G is splitting if it cuts Σ into two components, neither of which is homeomorphic to a disk. A splitting cycle has type k if the corresponding components have genera k and g− k. It was conjectured that G contains a splitting cycle (Barnette ’1982). We confirm this conjecture for an infinite family of triangulations by com...

We present a structure theorem for the subsurface projections of train track splitting sequences. For the proof we introduce induced tracks, efficient position, and wide curves. As a consequence of the structure theorem we prove that train track sliding and splitting sequences give quasi-geodesics in the train track graph; this generalizes a result of Hamenstädt [Invent. Math.].