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We introduce a modification of the Harary index where the contributions of vertex pairs are weighted by the sum of their degrees. After establishing basic mathematical properties of the new invariant, we proceed by finding the extremal graphs and investigating its behavior under several standard graph products.
One important task in the study of genome sequences and mutations is to determine densities of specific nucleotides and codons. The graphical representation of DNA sequences provide a simple way of viewing, storing, and comparing various sequences. In this paper, we first present for each kind of codon, a numerically representation as a 2D coordinate (x,y)… (More)
Polynomial interpolation can be used to obtain closed formulas for topological indices of infinite series of molecular graphs. The method is discussed and its advantages and limitations are pointed out. This is illustrated on fullerenes C 12k+4 and four topological indices: the Wiener index, the edge Wiener index, the eccentric connectivity index, and the… (More)
Wiener index was introduced by Harold Wiener in 1947. This index is the sum of distances between all vertices of a graph. The edge versions of Wiener index was introduced by Iranmanesh et al. in . In this paper, the first edge Wiener index of TUC 4 C 8 (S) nanotube is computed.
The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G. In this paper we compute this index for Splice and Link of two graphs. At least with use of Link of two graphs, we compute this index for a class of dendrimers. With this method, the NK index for other class of dendrimers can be computed… (More)
In this paper, a novel 3D graphical representation of DNA sequence based on codons is proposed. Since there is not loss of information due to overlapping and containing loops, this representation will be useful for comparison of different DNA sequences. This 3D curve will be convenient for DNA mutations comparison specially. In continues we give a numerical… (More)
A generalization of degree distance of graphs we recently proposed as a new topological index. In this paper, the new index is studied in trees, in unicyclic graphs of girth k and in some special classes of bicyclic graphs. Lower-bound and upper-bound values and analytical formulasto calculate this index in the studied graphs are given.