Weifan Wang, 王維凡, Yiqiao Wang, 葉永南, ADJACENT VERTEX DISTINGUISHING TOTAL COLORING OF GRAPHS WITH LOWER AVERAGE DEGREE, Taiwanese Journal of Mathematics, Vol. 12, No. 4, Dedicated to Professor Ko-Wei ...

For vertex-reinforced random walks, we extend results previously obtained on ℤ by Volkov [Ann. Probab. 29 (2001) 66–91] and by Basdevant, Schapira and Singh [Ann. Probab. 42 (2014) 527–558], and on ...

If k > 0, the vertex is a minimum turning point If k < 0, the vertex is a maximum turning point We can identify these properties from a quadratics graph or equation.