The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. The edge grafting operation on a graph is a kind of edge moving between the two pendent paths starting from the same vertex. In this paper we show how the graph energy change under the edge grafting operations. As the applications of this grafting method, we also obtain some new results on a conj...

Gutman et al. introduced the concepts of energy E (G) and Laplacian energy EL(G) for a simple graph G, and furthermore, they proposed a conjecture that for every graph G, E (G) is not more than EL(G). Unfortunately, the conjecture turns out to be incorrect since Liu et al. and Stevanović et al. constructed counterexamples. However, So et al. verified the conjecture for bipartite graphs. In the ...

This paper presents a methodology for deriving the system graph of a 3D mechanism from CAD models. That is, a linear graph that captures the energy flow in a system. This work is part of a larger research effort in composable simulation. In composable simulation, CAD models of system components are augmented with simulation models describing the component’s dynamic behavior in different energy ...

We propose a new approach for modelling the process of RNA folding as a graph transformation guided by the global value of free energy. Since the folding process evolves towards a configuration in which the free energy is minimal, the global behaviour resembles the one of a self-adaptive system. Each RNA configuration is a graph and the evolution of configurations is constrained by precise rule...