Computing Degree Based Topological Properties of Third Type of Hex-Derived Networks

• Main Authors: Chang-Cheng Wei, Haidar Ali, Muhammad Ahsan Binyamin, Muhammad Nawaz Naeem, Jia-Bao Liu
• Format: Article
• Language: English
• Published: MDPI AG 2019-04-01
• Series: Mathematics
• Subjects: general randić index; Harmonic index; augmented Zagreb index; atom–bond connectivity (<i>ABC</i>) index; geometric–arithmetic (<i>GA</i>) index; third type of hex-derived networks; <i>HDN<i>3</i>(r)</i>; <i>THDN<i>3</i>(r)</i>; <i>RHDN<i>3</i>(r)</i>; <i>CHDN<i>3</i>(r)</i>
• Online Access: https://www.mdpi.com/2227-7390/7/4/368

In chemical graph theory, a topological index is a numerical representation of a chemical network, while a topological descriptor correlates certain physicochemical characteristics of underlying chemical compounds besides its chemical representation. The graph plays a vital role in modeling and designing any chemical network. Simonraj et al. derived a new type of graphs, which is named a third type of hex-derived networks. In our work, we discuss the third type of hex-derived networks <inline-formula> <math display="inline"> <semantics> <mrow> <mi>H</mi> <mi>D</mi> <mi>N</mi> <mn>3</mn> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>T</mi> <mi>H</mi> <mi>D</mi> <mi>N</mi> <mn>3</mn> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>R</mi> <mi>H</mi> <mi>D</mi> <mi>N</mi> <mn>3</mn> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>H</mi> <mi>D</mi> <mi>N</mi> <mn>3</mn> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, and compute exact results for topological indices which are based on degrees of end vertices.