Find in Library

In 1997, Sierpinski graphs, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>, were obtained by Klavzar and Milutinovic. The graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula> represents the complete graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mi>k</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>(</mo><mi>n</mi><mo>,</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula> is known as the graph of the Tower of Hanoi. Through generalizing the notion of a Sierpinski graph, a graph named a generalized Sierpinski graph, denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>i</mi><mi>e</mi><mo>(</mo><mo>Λ</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula>, already exists in the literature. For every graph, numerous polynomials are being studied, such as chromatic polynomials, matching polynomials, independence polynomials, and the M-polynomial. For every polynomial there is an underlying geometrical object which extracts everything that is hidden in a polynomial of a common framework. Now, we describe the steps by which we complete our task. In the first step, we generate an M-polynomial for a generalized Sierpinski graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>i</mi><mi>e</mi><mo>(</mo><mo>Λ</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula>. In the second step, we extract some degree-based indices of a generalized Sierpinski graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>i</mi><mi>e</mi><mo>(</mo><mo>Λ</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> using the M-polynomial generated in step 1. In step 3, we generate the entropy of a generalized Sierpinski graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>i</mi><mi>e</mi><mo>(</mo><mo>Λ</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> by using the Randić index.