results the mean age in breathing technique with lavender and breathing technique alone were 25.5 ± 4.3 and 26 ± 4.9, respectively .two groups were comparable in this regards (p = 0.6), but the length of active phase in interventional group was 7.85 ± 3.85 hours and in the control group it was 9.88 ± 6.65 hours. the decrease of the length of labor in the active phase was higher in the experimen...

The vertex set of a digraph D is denoted by V (D). A c-partite tournament is an orientation of a complete c-partite graph. A digraph D is called cycle complementary if there exist two vertex disjoint cycles C1 and C2 such that V (D) = V (C1) ∪ V (C2), and a multipartite tournament D is called weakly cycle complementary if there exist two vertex disjoint cycles C1 and C2 such that V (C1) ∪ V (C2...

‎The Steiner distance of a graph‎, ‎introduced by Chartrand‎, ‎Oellermann‎, ‎Tian and Zou in 1989‎, ‎is a natural generalization of the‎ ‎concept of classical graph distance‎. ‎For a connected graph $G$ of‎ ‎order at least $2$ and $Ssubseteq V(G)$‎, ‎the Steiner‎ ‎distance $d(S)$ among the vertices of $S$ is the minimum size among‎ ‎all connected subgraphs whose vertex sets contain $S$‎. ‎Let $...

The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, we give formula for Merrifield-Simmons and Hosoya indices of some classes of cartesian product of two graphs K{_2}×H, where H is a path graph P{_n}, cyclic graph C{_n}, or star gra...

‎in this paper we give a characterization for all commutative‎ ‎rings with $1$ whose zero-divisor graphs are $c_4$-free.‎

A dynamic call graph is the invocation relation that represents a specific set of runtime executions of a program. Dynamic call graph extraction is a typical application of dynamic analysis to aid compiler optimization, performance analysis, program understanding, etc. In this paper, we empirically compare the results of nine Java dynamic call graph extractors quantitatively and qualitatively. ...

Despite persistent effort, there is no known technique for obtaining super-linear lower bounds for the computational complexity of the problems in P. Vassilevska Williams and Williams [38] introduce a fruitful approach to advance a better understanding of the computational complexity of the problems in P. In particular, they consider All Pairs Shortest Paths (APSP) and other fundamental problem...

n mathematical graph theory, coloring problems are ubiquitous. Dating back to the famous four-color map problem, both the theory and applications associated with graph coloring have a rich history. A standard problem in graph theory is to color a graph’s vertices with the fewest number of colors such that no two adjacent vertices have the same color. This article examines a complementary proble...

Computing semantic relatedness of natural language texts is a key component of tasks such as information retrieval and summarization, and often depends on knowledge from a broad range of real-world concepts and relationships. We address this knowledge integration issue with a method of computing semantic relatedness using personalized PageRank (random walks) on a graph derived from Wikipedia. T...

This paper introduces several related graph rewrite systems derived from known identities on classical structures within a †-symmetric monoidal category. First, we develop a rewrite system based on a single classical structure, and use it to develop a proof of the so-called “spider-theorem,” where a connected graph containing a single classical structure can be uniquely determined by the number...