Edge-adjacency index

Edge-Adjacency Index The edge-adjacency index, e, has been defined by Estrada [13] as follows  

Charge Indices Charge indices G and are calculated from the matrix product M=(A x D ), where D is the inverse square distance matrix [16]  

Charge terms (CTs) are defined as CTy = (M). - (M)7- . Then for each distance k that occurs in D, Gk is given by the following equation  

Correlations between charge indices and properties such as the dipole moment of hydrocarbons, the boiling point alkanes and alkanols, and the enthalpy of vaporization of alkanes have been studied [16]. 

Information-Theoretical Indices Information theory has been employed to define topological indices based on the Shannon equation [17]  

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APc3c = Pac (branched isomer)-/ c3c(normal isomer) [11] e edge-adjacency index [16]... 

The total edge adjacency index Ae (also known as Platt number, F [Platt, 1947 Platt, 1952]) is the sum over all entries of the edge adjacency matrix ... 

Platt number total edge adjacency index -> edge adjacency matrix PLS-based variable selection - variable selection P matrix -> bond order indices (O graphical bond order)... 

Platt number = total edge adjacency index —> edge adjacency matrix... 

This is derived from the partition of edge adjacency matrix elements according to their magnitude and is a trivial quantity because the zero entries do not contribute to the total edge adjacency index Ag ( Platt number), that is, the sum of all elements of the edge adjacency matrix, corresponding to tv ice the connection number N2 ... 

This is calculated by dividing the total information content on the edge adjacency magnitude by the total edge adjacency index Ae ... 

Proceeding from eqn. (13) and the correspondence between A and F indices, one observes that the index N2 corresponds to A. Hence, the Gordon-Scantlebury index has also the meaning of total edge adjacency of the graph. 

Estrada, E., Edge Adjacency Relationships and a Novel Topological Index Related to Molecular Volume. J. Chem. Inf. Comput. Sci., 1995 35, 31-33. 

This is the simplest graph invariant obtained from the -> adjacency matrix A, defined as the number of bonds in the -> molecular graph (7 where multiple bonds are considered as single edges. Bond number is calculated as half the - total adjacency index Ay ... 

ECN index -> electronegativity-based connectivity indices ECP index -> electronegativity-based connectivity indices edge adjacency matrix (E)... 

Ngs) [Gordon and Scantlebury, 1964] or Bertz branching index Bl), is the simplest graph-invariant obtained from the edge adjacency matrix which considers both vertices and edges and is calculated as ... 

From the edge adjacency matrix, a graph-theoretical invariant analogous to the -> Randic connectivity index was derived by Estrada [Estrada, 1995a] it is called edge connectivity index, denoted by e, and defined as ... 

More interesting is the -> edge-type Schultz index derived from both the edge distance matrix and the edge adjacency matrix. 

An edge-type Schultz index has been derived from the - edge adjacency matrix E and the - edge distance matrix [Estrada and Gutman, 1996 Estrada and Rodriguez, 1997] ... 

Estrada, E. (1995b). Edge Adjacency Relationships in Molecular Graphs Containing Heteroatoms A New Topological Index Related to Molar Volume. J.Chem.Inf.ComputScL, 35, 701-707. 

The total adjacency index Ay is a measure of the graph connectedness and is calculated as the sum of all the entries of the adjacency matrix of a molecular graph, vhich is tv ice the number B of graph edges [Harary, 1969a Rouvray, 1983] ... 

For example, the total adjacency index of 2-methylpentane isAy = l + 3 + 2 + 2 + l + l = 10, which is twice the number of edges equal to five in the H-depleted molecular graph of this molecule. Therefore, the number of entries equal to 1 in the adjacency matrix is 2B, while the number of entries equal to zero is — 2 B in particular, for acyclic graphs the total number of... 

Line graph of 2-methylpentane and its edge adjacency matrix, e, is the edge degree and e the edge connectivity index. 

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