Realizability of p‐point graphs with prescribed minimum degree, maximum degree, and line connectivity
Frank T. Boesch, Charles L. Suffel · Journal of Graph Theory · 1980
Abstract It is well known that certain graph‐theoretic extremal questions play a central role in the study of communication network vulnerability. Herein we consider a generalization of some of the classical results in this area. We define a (p, Δ, δ, λ) graph as a graph having p points, maximum degree Δ, minimum degree Δ, and line connectivity λ. An arbitrary quadruple of integers (a, b, c, d) is called (p, Δ, δ, λ) realizable if there is a (p, Δ, δ, λ) graph with p = a, Δ = b, Δ = c, and λ = d. Necessary and sufficient conditions for a quadruple to be (p, Δ, δ, λ) realizable are derived.