Inductive construction of 2-connected graphs for calculating the virial coefficients

Inductive construction of 2-connected graphs for calculating the virial coefficients

In this paper we give a method for constructing systematically all simple 2-connected graphs with n vertices from the set of simple 2-connected graphs with n-1 vertices, by means of two operations: subdivision of an edge and addition of a vertex. The motivation of our study comes from the theory of non-ideal gases and, more specifically, from the virial equation of state. It is a known result o...

An inductive construction of (2, 1)-tight graphs

The graphs G = (V,E) with |E| = 2|V | − ` that satisfy |E′| ≤ 2|V ′| − ` for any subgraph G′ = (V ′, E′) (and for ` = 1, 2, 3) are the (2, `)-tight graphs. The Henneberg–Laman theorem characterizes (2, 3)-tight graphs inductively in terms of two simple moves, known as the Henneberg moves. Recently, this has been extended, via the addition of a graph extension move, to the case of (2, 2)-tight s...

An Improved Correlation for Second Virial Coefficients of Pure Fluids

In the present work, a modified correlation is presented for the second virial coefficients of both polar and nonpolar fluids based on the corresponding states principle. The second virial coefficients of gaseous polar and non-polar compounds were calculated and compared with experimental data and with other correlations. Comparisons with the existing correlations show that the present work is ...

On Determination and Construction of Critically 2-Connected Graphs∗

Kriesell proved that every almost critical graph of connectivity 2 nonisomorphic to a cycle has at least 2 removable ears of length greater than 2. We improve this lower bound on the number of removable ears. A necessary condition for critically 2-connected graphs in terms of a forbidden minor is obtained. Further, we investigate properties of a special class of critically 2-connected series-pa...

Determination and Construction of Critically 2-Connected Graphs