By Dusanka Janezic, Ante Milicevic, Sonja Nikolic, Nenad Trinajstic

**Graph-Theoretical Matrices in Chemistry** offers a scientific survey of graph-theoretical matrices and highlights their power makes use of. This complete quantity is an up-to-date, prolonged model of a former bestseller that includes a chain of mathematical chemistry monographs. during this variation, approximately two hundred graph-theoretical matrices are included.

This moment variation is geared up just like the prior one―after an advent, graph-theoretical matrices are provided in 5 chapters: *The Adjacency Matrix and similar Matrices, prevalence Matrices, the space Matrix and comparable Matrices, precise Matrices, *and *Graphical Matrices*. each one of those chapters is by means of an inventory of references.

Among the matrices provided numerous are novel and a few are identified in simple terms to a couple. The houses and strength usefulness of the various awarded graph-theoretical matrices in chemistry have not begun to be investigated.

Most of the graph-theoretical matrices provided were used as assets of molecular descriptors often known as topological indices. they're really inquisitive about a different classification of graphs that represents chemical buildings related to molecules. because of its multidisciplinary scope, this e-book will entice a huge viewers starting from chemistry and arithmetic to pharmacology.

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**Example text**

12. 18. The degree of an edge is equal to the number of adjacent edges. 354 0 Summation of the elements in the upper (or lower) matrix-triangle gives the edge- connectivity index of G1 (Estrada, 1995a). , 1998). 18 The edge-degrees in G1 and vertex-degrees in L(G1). 15 THE SUM-VERTEX-CONNECTIVITY MATRIX The sum-vertex-connectivity matrix, denoted by vS, was introduced independently by Zhou and Trinajstić (2009, 2010a) and Randić et al. (2010). Randić et al. (2010) named this matrix the distance-weighted adjacency matrix.

Jiang, H. Liang, and F. Bai, New structural parameters and permanents of adjacency matrices of fullerenes, MATCH Commun. Math. Comput. Chem. 56 (2006) 131–139. M. Karelson, Molecular descriptors in QSAR/QSPR, Wiley-Interscience, New York, 2000. D. Kasum, N. Trinajstić, and I. Gutman, Chemical graph theory. III. On the permanental polynomial, Croat. Chem. Acta 54 (1981) 321–328. N. Kezele, L. V. Knop, S. Ivaniš, and S. Nikolić, Computing the variable vertexconnectivity index, Croat. Chem. Acta 75 (2002) 651–661.

21 A classical example of a pair of isospectral graphs. 5392}. 20 THE LAPLACIAN MATRIX The Laplacian matrix, denoted by L, is a real symmetric V × V matrix that may also be considered a kind of augmented vertex-adjacency matrix. 46) where d(i) is the degree of a vertex i. This matrix is also called the vertex-degree matrix (Todeschini and Consonni, 2000, 2009). 47) It should be noted that the smallest eigenvalue of L is always equal to zero, as a consequence of the special structure of the Laplacian matrix.