The Detour-Delta Matrix

The entries in the detour-delta matrix, denoted by DM, are related to the elements of the corresponding detour matrix as the entries of the vertex-distance-delta matrix are to the elements of the vertex-distance matrix. 

The following relationship is between the elements of the three matrices based on the longest graph-distances DM, DM, and DM  

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The detour-delta matrix, denoted as A, is another combinatorial matrix derived as the difference between the detour-path matrix Ap and the detour matrix A [Janezic, Milicevic... 

Detour-path matrix and detour-delta matrix for the H-depleted molecular graph of ethylbenzene tutu is the hyperdetour index and W/(Aa) is the Wiener-type index derived from the detour-delta matrix. 

The detour-delta matrix enumerates the number of all longest paths larger than unity between vertices i and j in a graph. The DM matrix of Gj (see structure A in Figure 2.1) is given below ... 

The most popular difference matrix is the -between the —> vertex degree matrix V and the -are the —> delta matrix, —> detour-delta matrix, matrix, and —> Cluj difference matrix. 

Opposite to the distance matrix is the —> detour matrix, where the entries correspond to the length of the longest path between two vertices. Other matrices related to the distance matrix are geometric distance/topolo cal distance quotient matrix, —> detour-distance combined matrix, distance/detour quotient matrix, —> distance-degree matrices, —> expanded distance matrices, —> distance-path matrix, delta matrix, —> distance sum layer matrix, —> distance-sequence matrix. 

The most common combinatorial matrices are derived from the distance matrix and detour matrix these are the distance-path matrix, detour-path matrix, delta matrix, and... 

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