Local edge domination critical graphs

✍ Scribed by Michael A. Henning; Ortrud R. Oellermann; Henda C. Swart

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 521 KB
• Volume: 161
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(95)00222-i

✦ Synopsis

Sumner and Blitch defined a graph G to be k-y-critical if 7(G) = k and 7(G + uv) = k -1 for each pair u, v of nonadjacent vertices of G. We define a graph to be k-( 7,d)-critical if 7(G) = k and 7(G + uv) = k -I for each pair u, v of nonadjacent vertices of G that are at distance at most d apart. The 2-(7, 2)-critical graphs are characterized. Sharp upper bounds on the diameter of 3-(7, 2)-and 4-(7, 2)-critical graphs are established and partial characterizations of 3-(7, 2)-critical graphs are obtained.