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On graphs containing a given graph as center

✍ Scribed by Fred Buckley; Zevi Miller; Peter J. Slater

Publisher: John Wiley and Sons
Year: 1981
Tongue: English
Weight: 367 KB
Volume: 5
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190050413

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We examine the problem of embedding a graph H as the center of a supergraph G, and we consider what properties one can restrict G to have. Letting A(H) denote the smallest difference ∣V(G)∣ ‐ ∣V(H)∣ over graphs G having center isomorphic to H it is demonstrated that A(H) ≤ 4 for all H, and for 0 ≤ i ≤ 4 we characterize the class of trees T with A(T) = i. for n ≥ 2 and any graph H, we demonstrate a graph G with point and edge connectivity equal to n, with chromatic number X(G) = n + X(H), and whose center is isomorphic to H. Finally, if ∣V(H)∣ ≥ 9 and k ≥ ∣V(H)∣ + 1, then for n sufficiently large (with n even when k is odd) we can construct a k‐regular graph on n vertices whose center is isomorphic to H.

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