The development of a mathematical theory for bond graphs continues with an analysis qf two areas crucial to the derivation of system equations,from a bond graph model. Matri.y representations of bond graph matroids ure exumined and used to provide a rigorous proof of the mathematical equivalence sf‘ the linear graph and bond graph modelling methods. The procedure of selecting causality by the m...

Let $G$ be a graph with vertex set $\{1,2,\ldots,n\}$. Its bond lattice, $BL(G)$, is sublattice of the partition lattice. The elements $BL(G)$ are partitions whose blocks induce connected subgraphs $G$.
 In this article, we consider graphs lattice consists only noncrossing partitions. We define family graphs, called triangulation property and show that any two produce isomorphic lattices. ...

In many applications that require physical interaction with humans or other physical environments, passivity is a useful property to have in order to improve safety and ease of use. Many mechatronic applications (e.g. teleoperators, robots that interact with humans) fall into this category. In this paper, we develop an approach to design passifying control laws for mechatronic components from a...

a graph that contains a hamiltonian cycle is called a hamiltonian graph. in this paper wecompute the first and the second geometric – arithmetic indices of hamiltonian graphs. thenwe apply our results to obtain some bounds for fullerene.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

We use quantum graphs as a model to study various mathematical aspects of the vacuum energy, such as convergence of periodic path expansions, consistency among different methods (trace formulae versus method of images) and the possible connection with the underlying classical dynamics. In our study we derive an expansion for the vacuum energy in terms of periodic paths on the graph and prove it...

In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star–triangle transformation, by transporting the box-crossing property across the family of isoradial ...

ABSTRACT: It is shown that an isolated thermal inertance does not obey the second law of thermodynamics. Consequently, such an element should not be used in physical systems theory. To eliminate the structural gap in the thermal domain of current physical systems theory, a new framework is introduced using Bond Graph concepts. These Thermodynamic Bond Graphs are the result of synthesis of metho...

Modified ANO-RCC basis sets are used to determine twelve molecular graphs of the Ehrenfest force for H2, CH4, CH2O, CH3NO, C2H2, C2H4, C3H3NO, N4H4, H2O, (H2O)2, (H2O)4 and (H2O)6. The molecular graphs include all types of topological critical points and a mix of bonding types is chosen to include sigma-, π- and hydrogen-bonding. We then compare a wide range of point properties: charge density,...

Bond-Graphs based representation and genetic programming based search and synthesis can be combined for automated design of mechatronic or multi domain dynamic systems. This design scheme can be turned into an intelligent automated design system by introducing a dynamic database or knowledge library of relevant information (gathered through design experience) which tends to help the designer in...