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Dobrynin, Andrey A.; Gutman, Iván; Klavžar, Sandi; Žigert, Petra

doi:10.1023/a:1016290123303

Cited by 247 publications

(40 citation statements)

References 62 publications

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“…One of the most famous topological indices is Wiener index, defined as the sum of all distances between different vertices of a molecular graph, introduced by Wiener in 1947 (see [10]) in a paper concerned with boiling points of alkanes. In a research that followed many other useful properties of Wiener index were discovered (for a survey of mathematical properties and chemical applications of Wiener index one can look into [3,4,7]). But, contrary to chemical intuition, the contribution of close pairs of vertices to the overall value of the index was much smaller than that of distant vertices.…”

Section: Introductionmentioning

confidence: 99%

Extremal unicyclic graphs with respect to additively weighted Harary index

Sedlar¹

2015

Miskolc Math Notes

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Abstract. In this paper we define cycle-star graph CS k;n k to be a graph on n vertices consisting of the cycle of length k and n k leafs appended to the same vertex of the cycle. Also, we define cycle-path graph CP k;n k to be a graph on n vertices consisting of the cycle of length k and of path on n k vertices whose one end is linked to a vertex on a cycle. We establish that cyclestar graph CS 3;n 3 is the only maximal graph with respect to additively weighted Harary index among all unicyclic graphs on n vertices, while cycle-path graph CP 3;n 3 is the only minimal unicyclic graph (here n must be at least 5): The values of additively weighted Harary index for extremal unicyclic graphs are established, so these values are the upper and the lower bound for the value of additively weighted Harary index on the class of unicyclic graphs on n vertices.

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Section: Introductionmentioning

confidence: 99%

Extremal unicyclic graphs with respect to additively weighted Harary index

Sedlar¹

2015

Miskolc Math Notes

View full text Add to dashboard Cite

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“…A topological index is a real number associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Wiener index [10][11][12] is the first topological index introduced by chemist H. Wiener in 1947. This index is defined as the sum of all topological distances between the pair of vertices.…”

Section: Introductionmentioning

confidence: 99%