Two sets of graceful graphs
β Scribed by Charles Delorme
- Publisher
- John Wiley and Sons
- Year
- 1980
- Tongue
- English
- Weight
- 109 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
We give graceful numberings to the following graphs: (a) the union of n K4 having one edge in common, in other words the join of K2 and the union of n disjoint K2 and (b) the union of n C4 having one edge in common, in other words the product of K2 and K,,", with n + l not a multiple of 4.
π SIMILAR VOLUMES
It is shown that the graph kc, (consisting of k 4-cycles) has an a-valuation (a stronger form of the graceful valuation) for every positive integer k # 3. The graph 3C, is known to be graceful but it does not have an a-valuation.
It is shown in this note that it can be recognized in polynomial time whether the vertex set of a finite undirected graph can be partitioned into one or two independent sets and one or two cliques. Such graphs generalize bipartite and split graphs and the result also shows that it can be recognized
Andreae, T., M. Schughart and Z. Tuza, Clique-transversal sets of line graphs and complements of line graphs, Discrete Mathematics 88 (1991) 11-20. A clique-transversal set T of a graph G is a set of vertices of G such that T meets all maximal cliques of G. The clique-transversal number, denoted t,(
Topp, J., Graphs with unique minimum edge dominating sets and graphs with unique maximum independent sets of vertices, Discrete Mathematics 12 1 (1993) 199-210. A set I of vertices of a graph G is an independent set if no two vertices of I are adjacent. A set M of edges of G is an edge dominating s