| Summary: | Let <i>G</i> be a simple, connected and undirected graph. The atom-bond connectivity index (<inline-formula><math display="inline"><semantics><mrow><mi>A</mi><mi>B</mi><mi>C</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula>) and Randić index (<inline-formula><math display="inline"><semantics><mrow><mi>R</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula>) are the two most well known topological indices. Recently, Ali and Du (2017) introduced the difference between atom-bond connectivity and Randić indices, denoted as <inline-formula><math display="inline"><semantics><mrow><mi>A</mi><mi>B</mi><mi>C</mi><mo>−</mo><mi>R</mi></mrow></semantics></math></inline-formula> index. In this paper, we determine the fourth, the fifth and the sixth maximum chemical trees values of <inline-formula><math display="inline"><semantics><mrow><mi>A</mi><mi>B</mi><mi>C</mi><mo>−</mo><mi>R</mi></mrow></semantics></math></inline-formula> for chemical trees, and characterize the corresponding extremal graphs. We also obtain an upper bound for <inline-formula><math display="inline"><semantics><mrow><mi>A</mi><mi>B</mi><mi>C</mi><mo>−</mo><mi>R</mi></mrow></semantics></math></inline-formula> index of such trees with given number of pendant vertices. The role of symmetry has great importance in different areas of graph theory especially in chemical graph theory.
|
|---|