𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the hamiltonian index and the radius of a graph

✍ Scribed by Marko LovrečičSaraẑin


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
316 KB
Volume
182
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis


Catlin et al. [1, Corollary 9A]

characterised the graphs G with the property that ham(G) > rad(G) + 1 where ham(G) and rad(G) stand for the hamiltonian index and the radius of G, respectively. Here a slightly stronger result is presented. In effect, the graphs for which ham(G) > rad(G) holds are characterised in a similar way.


📜 SIMILAR VOLUMES


On line graphs and the hamiltonian index
✍ Ronald J. Gould 📂 Article 📅 1981 🏛 Elsevier Science 🌐 English ⚖ 812 KB

## An extension of CI theorem of Chamhnd and Wall is obtained and, with it, a bound on the lamiltoniau index h(G) of a connected graph G (other than a path) is determined. As a tonsequence, it is Fhown that if G is homogeneously traceable, then h(Gj ~2.

On the hamiltonian path graph of a graph
✍ George R. T. Hendry 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 491 KB 👁 1 views

The hamiltonian path graph H(F) of a graph F is that graph having the same vertex set as F and in which two vertices u and u are adjacent if and only if F contains a hamiltonian u -u path. First, in response to a conjecture of Chartrand, Kapoor and Nordhaus, a characterization of nonhamiltonian grap

On the radius of graphs
✍ Jochen Harant; Hansjoachim Walther 📂 Article 📅 1981 🏛 Elsevier Science 🌐 English ⚖ 200 KB
On the spectral radius of a directed gra
✍ Kwapisz, Jaroslaw 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 314 KB 👁 2 views

We provide upper estimates on the spectral radius of a directed graph. In particular w e prove that the spectral radius is bounded by the maximum of the geometric mean of in-degree and out-degree taken over all vertices.