Normal components, Kekule patterns, and Clar patterns in plane bipartite graphs

As a general case of molecular graphs of polycyclic alternant hydrocarbons, we consider a plane bipartite graph G with a Kekule pattern (perfect matching). An edge of G is called nonfixed if it belongs to some, but not all, perfect matchings of G. Several criteria in terms of resonant cells for determining whether G is elementary (i.e., without fixed edges) are reviewed. By applying perfect matching theory developed in plane bipartite graphs, in a unified and simpler way we study the decomposition of plane bipartite graphs with fixed edges into normal components, which is shown useful for resonance theory, in particular, cell and sextet polynomials. Further correspondence between the Kekule patterns and Clar (resonant) patterns are revealed

Flip Distances Between Graph Orientations

International audienc

Temporal causality and the dynamics of democracy, emigration and real income in Fiji

This study is the first to explore temporal causality between democracy, emigration and real income in Fiji within a multivariate cointegration model. We find three long run relationships between democracy, emigration and real income. In the long run there is evidence that migration and democracy Granger cause real GDP in Fiji; real GDP and democracy Granger cause migration from Fiji and that real GDP and migration Granger cause democracy in Fiji. In the short run we find unidirectional Granger causality running from migration to real GDP and from democracy to real GDP, but neutrality between democracy and migration in the short run. We also extend the analysis to examine the degree of exogeneity of the variables beyond the sample period through considering the decomposition of variance and impulse response functions.Fiji, democracy, migration, cointegration, causality,