On Equi-Cardinal, Restrictions of a Graph
Canadian mathematical bulletin, Tome 7 (1964) no. 3, pp. 369-375
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A graph G is an ordered pair (V, E) where V is a set of objects called vertices, and E is a set of unordered pairs of vertices (v, v') in which each such pair can occur at most once in E, and if (v, v') ε E then v ≠ v'. The order of G is the cardinality of the set V, and the degree δ(v) of an element v ε V is the number of elements of E which contain v. G is said to be regular of degree d if δ(v) = d for each v ε V. G is a complete graph if E contains every pair of elements of V. A graph H = (V', E') is a partial graph of G=(V, E) if V' ⊆ v and E' ⊆ E. H is a restriction of G if H is a partial graph of G in which V' = V. Let S = { e1, ..., el} be a subset of E such that ej={vj-1, vj} for 1 ≤j ≤l.
Beatty, J. C.; Miller, R. E. On Equi-Cardinal, Restrictions of a Graph. Canadian mathematical bulletin, Tome 7 (1964) no. 3, pp. 369-375. doi: 10.4153/CMB-1964-034-7
@article{10_4153_CMB_1964_034_7,
author = {Beatty, J. C. and Miller, R. E.},
title = {On {Equi-Cardinal,} {Restrictions} of a {Graph}},
journal = {Canadian mathematical bulletin},
pages = {369--375},
year = {1964},
volume = {7},
number = {3},
doi = {10.4153/CMB-1964-034-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1964-034-7/}
}
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