✦ LIBER ✦

Reconstructing the number of copies of a valency-labeled finite graph in an infinite graph

✍ Scribed by A. J. H. King; C. St. J. A. Nash-Williams

Publisher: John Wiley and Sons
Year: 1994
Tongue: English
Weight: 489 KB
Volume: 18
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190180202

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Suppose that G, H are infinite graphs and there is a bijection Ψ; V(G) Ψ V(H) such that G ‐ ξ ≅ H ‐ Ψ(ξ) for every ξ ∼ V(G). Let J be a finite graph and /(π) be a cardinal number for each π ≅ V(J). Suppose also that either /(π) is infinite for every π ≅ V(J) or J has a connected subgraph C such that /(π) is finite for every π ≅ V(C) and every vertex in V(J)/V(C) is adjacent to a vertex of C. Let (J, I, G) be the set of those subgraphs of G that are isomorphic to J under isomorphisms that map each vertex π of J to a vertex whose valency in G is /(π). We prove that the sets (J, I, G), m(J, I, H) have the same cardinality and include equal numbers of induced subgraphs of G, H respectively.

📜 SIMILAR VOLUMES

Note on the reconstruction of infinite g

Note on the reconstruction of infinite graphs with a fixed finite number of components

✍ Thomas Andreae 📂 Article 📅 1982 🏛 John Wiley and Sons 🌐 English ⚖ 169 KB 👁 1 views

For every positive integer c , we construct a pair G, , H, of infinite, nonisomorphic graphs both having exactly c components such that G, and H, are hypomorphic, i.e., G, and H, have the same families of vertex-deleted subgraphs. This solves a problem of Bondy and Hemminger. Furthermore, the pair G

An upper bound on the number of cliques

An upper bound on the number of cliques in a graph

✍ Martin Farber; Mihály Hujter; Zsolt Tuza 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 252 KB 👁 1 views

Calculating the number of spanning trees

Calculating the number of spanning trees in a labeled planar molecular graph whose inner dual is a tree

✍ P. E. John; R. B. Mallion 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 496 KB 👁 3 views

The quantum mechanical relevance of the concept of a spanning tree extant within a given molecular graph-specifically, one that may be considered to represent the carbon-atom connectivity of a particular (planar) conjugated system-was first explicitly pointed out by Professor Roy McWeeny in his now-

On the number of (r,r+1)- factors in an

On the number of (r,r+1)- factors in an (r,r+1)-factorization of a simple graph

✍ A. J. W. Hilton 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 113 KB 👁 1 views

## Abstract For integers __d__≥0, __s__≥0, a (__d, d__+__s__)‐__graph__ is a graph in which the degrees of all the vertices lie in the set {__d, d__+1, …, __d__+__s__}. For an integer __r__≥0, an (__r, r__+1)‐__factor__ of a graph __G__ is a spanning (__r, r__+1)‐subgraph of __G__. An (__r, r__+1)‐