On the Number of Spanning Trees of Graphs
On the Number of Spanning Trees of Graphs
We establish some bounds for the number of spanning trees of connected graphs in terms of the number of vertices<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>, the number of edges<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>, maximum vertex degree<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mo>Δ</mml:mo></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math>, minimum vertex degree<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mo stretchy="false">(</mml:mo><mml:mi>δ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>, first Zagreb index<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" …