D-MAX - Matrix of Dominant Distances in a Graph

作者：Randic Milan^*

来源：MATCH-Communications in Mathematical and in Computer Chemistry, 2013, 70(1): 221-238.

We are introducing a novel distance-type matrix for graphs, referred to as D-MAX, which is constructed from the distance matrix of a graph be selecting for each row and each column only the largest distances. This matrix can be viewed as opposite to the adjacency matrix, which can be constructed from the distance matrix be selecting for each row and each column only the smallest distances, which correspond to adjacent vertices. We have illustrated the novel matrix for linear n-alkanes and n-star graphs, as well as the nine isomers of heptane. In the case of isomers, the matrix appears very sensitive on the branching pattern of molecular graphs. Therefore it may be of interest for characterizing of molecular shapes. On the other hand, in view that selected invariants of D-MAX for structurally related molecules could be significantly different, it appears that such invariants of D-MAX can be of interest in testing graphs for isomorphism.

• 出版日期2013