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Pancyclic and panconnected line graphs

✍ Scribed by Abdelhamid Benhocine; Jean-Luc Fouquet

Publisher: John Wiley and Sons
Year: 1987
Tongue: English
Weight: 716 KB
Volume: 11
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190110313

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✦ Synopsis

Let G be a graph of order n 2 3. We prove that if G is k-connected ( k 2 2) and the degree sum of k + 1 mutually independent vertices of G is

We also prove that if G is such that the degree sum of every 2 adjacent vertices is at least n , then L ( G ) is panconnected with some exceptions.

📜 SIMILAR VOLUMES

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Clark proved that L(G) is hamiltonian if G is a connected graph of order n 2 6 such that deg u + deg v 2 n -1p(n) for every edge uv of G, where p(n) = 0 if n is even and p(n) = 1 if n is odd. Here it is shown that the bound n -1 -dn) can be decreased to (2n + 1)/3 if every bridge of G is incident wi

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A graph is k-triangular if each edge is in at least k triangles. Triangular is a synonym for l-triangular. It is shown that the line graph of a triangular graph of order at least 4 is panconnected if and only if it is 3-connected. Furthermore, the line graph of a k-triangular graph is k-harniltonian

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✍ Sun-Yuan Hsieh; Tsong-Jie Lin 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 266 KB

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✍ Zeng Min Song 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 324 KB

## Abstract Let __D__ be an oriented graph of order __n__ ≧ 9 and minimum degree __n__ − 2. This paper proves that __D__ is pancyclic if for any two vertices __u__ and __v__, either __uv__ ≅ __A(D)__, or __d__~__D__~^+^(__u__) + __d__~__D__~^−^(__v__) ≧ __n__ − 3.

Weakly pancyclic graphs

✍ Brandt, Stephan; Faudree, Ralph; Goddard, Wayne 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 517 KB

In generalizing the concept of a pancyclic graph, we say that a graph is ''weakly pancyclic'' if it contains cycles of every length between the length of a shortest and a longest cycle. In this paper it is shown that in many cases the requirements on a graph which ensure that it is weakly pancyclic