Some new results on the face index of certain polycyclic chemical networks

Ricai Luo; Khadija Dawood; Muhammad Kamran Jamil; Muhammad Azeem; Ricai Luo; Khadija Dawood; Muhammad Kamran Jamil; Muhammad Azeem

doi:10.3934/mbe.2023348

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 5: 8031-8048. doi: 10.3934/mbe.2023348

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Some new results on the face index of certain polycyclic chemical networks

1.
School of Mathematics and Physics, Hechi University, Yizhou, Guangxi 456300, China
2.
Department of Mathematics, Riphah International University Lahore, Pakistan

Academic Editor: Jose M. Rodriguez

Received: 11 January 2023 Revised: 01 February 2023 Accepted: 02 February 2023 Published: 23 February 2023

Silicate minerals make up the majority of the earth's crust and account for almost 92 percent of the total. Silicate sheets, often known as silicate networks, are characterised as definite connectivity parallel designs. A key idea in studying different generalised classes of graphs in terms of planarity is the face of the graph. It plays a significant role in the embedding of graphs as well. Face index is a recently created parameter that is based on the data from a graph's faces. The current draft is utilizing a newly established face index, to study different silicate networks. It consists of a generalized chain of silicate, silicate sheet, silicate network, carbon sheet, polyhedron generalized sheet, and also triangular honeycomb network. This study will help to understand the structural properties of chemical networks because the face index is more generalized than vertex degree based topological descriptors.
- silicate networks,
- polyhedron generalized sheet,
- triangular honeycomb network,
- carbon sheet,
- face index,
- topological index
Citation: Ricai Luo, Khadija Dawood, Muhammad Kamran Jamil, Muhammad Azeem. Some new results on the face index of certain polycyclic chemical networks[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 8031-8048. doi: 10.3934/mbe.2023348

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Abstract

Silicate minerals make up the majority of the earth's crust and account for almost 92 percent of the total. Silicate sheets, often known as silicate networks, are characterised as definite connectivity parallel designs. A key idea in studying different generalised classes of graphs in terms of planarity is the face of the graph. It plays a significant role in the embedding of graphs as well. Face index is a recently created parameter that is based on the data from a graph's faces. The current draft is utilizing a newly established face index, to study different silicate networks. It consists of a generalized chain of silicate, silicate sheet, silicate network, carbon sheet, polyhedron generalized sheet, and also triangular honeycomb network. This study will help to understand the structural properties of chemical networks because the face index is more generalized than vertex degree based topological descriptors.

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