With the wide application of blockchain in financial field, rise various types cybercrimes has brought great challenges to security blockchain. In order better understand this emerging market and explore more efficient countermeasures for effective supervision, it is imperative track transactions on blockchain-based systems. Due openness Ethereum, we can easily access publicly available transac...

Tay [6] characterized the multigraphs which can be realized as infinitesimally rigid d-dimensional body-and-bar frameworks. Subsequently, Tay [7] and Whiteley [11] independently characterized the multigraphs which can be realized as infinitesimally rigid d-dimensional body-and-hinge frameworks. We adapt Whiteley’s proof technique to characterize the multigraphs which can be realized as infinite...

T-S. Tay and W. Whiteley independently characterized the multigraphs which can be realized as an infinitesimally rigid d-dimensional body-and-hinge framework. In 1984 they jointly conjectured that each graph in this family can be realized as an infinitesimally rigid framework with the additional property that the hinges incident to each body lie in a common hyperplane. This conjecture has becom...

Goodness of fit tests for two probabilistic multigraph models are presented. The first model is random stub matching given fixed degrees (RSM) so that edge assignments to vertex pair sites dependent, and the second independent (IEA) according a common probability distribution. Tests performed using goodness measures between multiplicity sequence an observed multigraph, expected one simple or co...

Gagliardi et al. (1996, unpublished manuscript) defined an irregular multigraph to be a loopless multigraph with degree sequence n, n 1 . . . . . 1, and they posed the problem of determining the number of different irregular multigraphs f , on n vertices. In Gagliardi et al. (1996) they showed that if n 0 or 3 (mod 4) then f , > n 1. In this note our aim is to show that there are constants 1 < ...