Chartrand, Gary; Holbert, Karen S.; Oellermann, Ortrud R.; Swart, Henda C. \(F\)-degrees in graphs. (English) Zbl 0643.05055 Ars Comb. 24, 133-148 (1987). Let \(F\) and \(G\) be graphs. The \(F\)-degree of a vertex \(v\) in \(G\), denoted by \(F\)-\(\deg v\) is the number of subgraphs of \(G\) isomorphic to \(F\) that contain \(v\). For example, the \(K_ 2\)-degree of a vertex \(v\) in any graph \(G\) is simply the degree of \(v\) in \(G\). A graph \(G\) is \(F\)-regular of degree \(k\) if every vertex of \(G\) has \(F\)-degree \(k\). The four authors investigate \(F\)-regular graphs and specify some classes of \(F\)-regular graphs. Furthermore, they prove the existence of \(F\)-irregular graphs for special \(F\) and conjecture that there exists an \(F\)-irregular graph for every connected graph \(F\) of order at least 3. Reviewer: R.Bodendiek Cited in 8 Documents MSC: 05C99 Graph theory 05C75 Structural characterization of families of graphs Keywords:regular graphs PDFBibTeX XMLCite \textit{G. Chartrand} et al., Ars Comb. 24, 133--148 (1987; Zbl 0643.05055)