‎an  oriented perfect path double cover (oppdc) of a‎ ‎graph $g$ is a collection of directed paths in the symmetric‎ ‎orientation $g_s$ of‎ ‎$g$ such that‎ ‎each arc‎ ‎of $g_s$ lies in exactly one of the paths and each‎ ‎vertex of $g$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎maxov{'a} and ne{v{s}}et{v{r}}il (discrete‎ ‎math‎. ‎276 (2004) 287-294) conjectured that ...

This research is based on an energy audit of two multi-unit residential buildings (MURBs) located in Toronto, Canada. Energy consumption (gas and electricity) data were extracted from the bills for a consecutive period three years. The then normalized to account variations weather conditions. Conclusions drawn correlation analyses between kWh, cooling degree days (CDDs), heating (HDDs), which c...