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The Common Vertex Matrix

FIGURE 4.12 The conveniently labeled tree T2 representing the carbon skeleton of 2,3-dimethylhexane. [Pg.106]

Randid et al. (2013a) illustrated on smaller alkanes that CVM is sensitive to branching, and that the ordered row sums of CVM may facilitate solving a graph isomerism problem for acyclic graphs. Randid and his coworkers (Randid et al., 2013b) used the common vertex matrix for novel characterization of the central vertex or vertices in acyclic and cyclic graphs. [Pg.107]

Amic and N. Trinajstic, On the detour matrix, Croat. Chem. Acta 68 (1995) 53-62. [Pg.107]

Lukovits, S. Nikolic, and N. Trinajstid, Resistance-distance matrix A computional algorithm and its apphcation, Int. J. Quantum Chem. 90 (2002) 166-176. A.T. Balaban, Topological indices based on topological distances in molecular graphs. Pure Appl. Chem. 55 (1983) 199-206. [Pg.107]

Balaban, Chemical graphs. 48. Topological index J for heteroatom-containing molecules taking in to account periodicities of element properties, MATCH Commun. Math. Comput. Chem. 21 (1986) 115-122. [Pg.107]


One such new theory has been the common vertex matrix [2], which has led to a novel approach to graph eccentricities and network eccentricities, based on the count of pairs of vertices at equal distance from each vertex in a graph [3]. A preliminary study has shown that the connectivity-type index based on the vertex centrality values displays considerable discriminatory power in differentiating between similar structures, including very similar structures among isomers. The discriminatory power of a centrality-based connectivity index exceeds visibly the discriminatory power of Balaban s J index [4-6], which is a distance matrix analog of the connectivity index. [Pg.219]

The Adjacency Matrix, the Distance Matrix, the Wiener Matrix, the Common Vertex Matrix, and the Pseudo-Distance Matrix of 3-Methylhexane and Their Row Sums... [Pg.223]

In Table 8.2, we show the row sums for the adjacency matrix, the (sparse) Wiener matrix, the common vertex matrix, and the -Dim. The elements of the Wiener matrix are defined as = fl x Uj if the vertices i and j are connected, where a, and aj are the number of vertices closer to vertex i and j, respectively, and = 0 otherwise. [Pg.226]

The elements of the common vertex matrix are defined as a, = where is the number of pairs of vertices at the same distance from vertex a , j = pij if i and j are connected where Pij is the number of pairs of vertices at the same distance from both a, and aj, and = 0 otherwise. [Pg.226]

In the original publication on the common vertex matrix [3], the diagonal elements were assumed to be zero. [Pg.226]

The corresponding common vertex matrix CVM of T2 (see Figure 2.19) is shown below ... [Pg.106]

It does appear that novel matrices of graphs, such as, for example, the recently constructed -dimensional (pseudo) distance matrix [7], the D ax matrix containing only the maximal distances in each row and each column of the distance matrix [8,9], and the already mentioned common vertex matrix [2], may lead to a number of novel graph descriptors, some of which may be of interest in the search for structurally highly similar molecules. [Pg.220]

Observe that no member of R(n), other than the zero matrix, can belong to B n), since the sum of the entries in a 0 is necessarily >0 thus, R(n)nB n) =(0). In the geometric representation r[B(n)] was visualized as a cone in R with vertex at the origin we will see from Theorem 8 below that n [B( )] lies on a linear subspace going through the origin and having no other point in common with tc [R (m)] ... [Pg.47]


See other pages where The Common Vertex Matrix is mentioned: [Pg.222]    [Pg.222]    [Pg.227]    [Pg.159]    [Pg.229]    [Pg.171]    [Pg.5]    [Pg.886]    [Pg.171]    [Pg.39]    [Pg.253]    [Pg.2511]    [Pg.30]    [Pg.283]    [Pg.431]    [Pg.189]    [Pg.421]    [Pg.70]   


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