  An analytical approach is developed to obtain the exact expressions for the
two-point resistance, and the total effective resistance of the complete graph
minus $N$ edges of the opposite vertices. These expressions are written in
terms of certain numbers that we introduced which we call the Bejaia and the
Pisa numbers, these numbers are the natural generalizations of the bisected
Fibonacci and Lucas numbers. The correspondence between random walks and the
resistor networks is then used to obtain the exact expressions for the the
first passage and mean first passage times on this graph.
