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We determine the smallest and the largest number of (A,B,2C)-edge colourings in trees. We prove that the star is a unique tree that maximizes the number of all of the (A,B,2C)-edge colourings and that the path is a unique tree that minimizes it

journal of applied mathematics

Extremal Trees with respect to Number of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>B</mml:mi><mml:mo>,</mml:mo><mml:mn fontstyle="italic">2</mml:mn><mml:mi>C</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-Edge Colourings

Extremal Trees with respect to Number of(A,B,2C)-Edge Colourings