On reverse degree distance
✍ Scribed by Bo Zhou; Nenad Trinajstić
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 141 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0259-9791
No coin nor oath required. For personal study only.
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We prove that in a graph of order n and minimum degree d, the mean distance µ must satisfy This asymptotically confirms, and improves, a conjecture of the computer program GRAFFITI. The result is close to optimal; examples show that for any d, µ may be larger than n/(d + 1).
95-99 mistakenly attributes the computer program GRAFFITI to Fajtlowitz and Waller, instead of just Fajtlowitz. (Our apologies to Siemion Fajtlowitz.) Note also that one of the ''flaws'' we note for Conjecture 62 (that it was made for graphs regular of degree d, vice graphs of minimum degree d) was
## Abstract As counterexamples to a conjecture of Randić, pairs of nonisomorphic trees with the same collections of distance degree sequences are presented.
The average distance µ(G) of a connected graph G of order n is the average of the distances between all pairs of vertices of G, i.e., µ(G) = ( n 2 ) -1 {x,y}⊂V (G) d G (x, y), where V (G) denotes the vertex set of G and d G (x, y) is the distance between x and y. We prove that every connected graph