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Basic Chemical Graph Theory

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Multi-shell Polyhedral Clusters

Part of the book series: Carbon Materials: Chemistry and Physics ((CMCP,volume 10))

Abstract

Graph Theory applied in Chemistry is called Chemical Graph Theory. This interdisciplinary science takes problems (like isomer enumeration, structure elucidation, etc.) from Chemistry and solve them by Mathematics (using tools from Graph Theory, Set Theory or Combinatorics), thus influencing both Chemistry and Mathematics. This chapter introduces to basic definitions in Graph Theory: graph, walk, path, circuit, planar graph, graph invariant, vertex degree, chemical graph, etc. Then topological matrices are introduced: adjacency, distance, detour, combinatorial matrices, Wiener and Cluj matrices, walk matrix operator (combining three square matrices), reciprocal distance, and layer/shell matrices, on which the centrality indices are defined. Some info about topological symmetry is also presented.

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Authors and Affiliations

  1. Department of Chemistry, Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, Cluj-Napoca, Romania

    Mircea Vasile Diudea

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  1. Mircea Vasile Diudea
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Diudea, M.V. (2018). Basic Chemical Graph Theory. In: Multi-shell Polyhedral Clusters. Carbon Materials: Chemistry and Physics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-64123-2_1

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