Given a graph G, its energy E G is defined as the sum of the absolute values of the eigenvalues of G. The concept of the energy of a graph was introduced in the subject of chemistry by I. Gutman, due to its relevance to the total π-electron energy of certain molecules. In this paper, we show that if
Interior graphs of maximal outerplane graphs
✍ Scribed by Sandra M Hedetniemi; Andrzej Proskurowski; Maciej M Sysło
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 631 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0095-8956
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Let χ l (G), χ l (G), χ l (G), and (G) denote, respectively, the list chromatic number, the list chromatic index, the list total chromatic number, and the maximum degree of a non-trivial connected outerplane graph G. We prove the following results. ( 1 and only if G is an odd cycle. This proves the
Caccetta, L. and K. Vijayan, Maximal cycles in graphs, Discrete Mathematics 98 (1991) l-7. Let G be a simple graph on n vertices and m edges having circumference (longest cycle length) 1. Woodall determined some time ago the maximum possible value of m. The object of this paper is to give an altern
## Abstract The center of a graph is defined to be the subgraph induced by the set of vertices that have minimum eccentricities (i.e., minimum distance to the most distant vertices). It is shown that only seven graphs can be centers of maximal outerplanar graphs.