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Realizability of p ‐point graphs with prescribed minimum degree, maximum degree, and line connectivity
Author(s) -
Boesch F. T.,
Suffel C. L.
Publication year - 1980
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190040404
Subject(s) - mathematics , degree (music) , combinatorics , realizability , line graph , graph , discrete mathematics , generalization , algorithm , mathematical analysis , physics , acoustics
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.