A covariant path integral calculation of the even spin structure contribution to the one-loop N-graviton scattering amplitude in the type-II superstring theory is presented. The apparent divergence of the N = 5 amplitude is resolved by separating it into twelve independent terms corresponding to different orders of inserting the graviton vertex operators. Each term is well defined in an appropr...

Large scale-free graphs are famously difficult to process efficiently: the skewed vertex degree distribution makes it difficult to obtain balanced partitioning. Our research instead aims to turn this into an advantage by partitioning the workload to match the strength of the individual computing elements in a Hybrid, GPU-accelerated architecture. As a proof of concept we focus on the direction-...

The Green-Naghdi equations are a shallow water waves model which play important roles in nonlinear wave fields. By using the trial equation method and Complete discrimination system for polynomial we obtained classification of travelling patterns. Among those patterns, new singular patterns double periodic first time. And draw graphs help us to understand dynamics behaviors intuitionally.

In this paper, the concept of incidence domination number of graphs  is introduced and the incidence dominating set and  the incidence domination number  of some particular graphs such as  paths, cycles, wheels, complete graphs and stars are studied.

Abstract In this paper we investigate the $$ L^1 L 1 -Liouville property, underlining its connection with stochastic completeness and other structural features of graph. We give a characterization property in terms Green function graph use it to prove equivalence on mod...

A graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. In this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.

The energy of signed graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two signed graphs are said to be equienergetic if they have same energy. In the literature the construction of equienergetic signed graphs are reported. In this paper we obtain the characteristic polynomial and energy of the join of two signed graphs and thereby we give another construction ...

The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...

In this paper we define the removable cycle that, if $Im$ is a class of graphs, $Gin Im$, the cycle $C$ in $G$ is called removable if $G-E(C)in Im$. The removable cycles in Eulerian graphs have been studied. We characterize Eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for Eulerian graph to have removable cycles h...