On determination of graph G whose bond lattice ℒ(G) is modular

✍ Scribed by Morimasa Tsuchiya

• Publisher: Elsevier Science
• Year: 1985
• Tongue: English
• Weight: 121 KB
• Volume: 56
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(85)90195-5

✦ Synopsis

We shall prove that a bond lattice .Y(G) of a graph G is Boolean if and only if G is a forest, and that a bond lattice .~(G) is modular if and only if G has no cycle of length n > 3.

In this paper, we consider finite undirected simple graphs. For a graph G, V(G) and E(G) denote the set of vertices and the set of edges of G, respectively. For an edge-subset Sc=E(G), (S)E denotes the subgraph generated by S. For