✦ LIBER ✦

Extending a function on a graph

✍ Scribed by D.F. Robinson

Publisher: Elsevier Science
Year: 1973
Tongue: English
Weight: 913 KB
Volume: 6
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(73)90038-1

No coin nor oath required. For personal study only.

✦ Synopsis

Let G be a graph with vertex set V, and let h be a function mapping a subset U of I/ into the real numbers R. If f is a function from I' to R, we define S y) to be the sum of If(b)f(a)1 over all edges {a, b} of G. A best extension of h is such a function f with f(x) = h(x) for

x E U and minimum 6 u>. We show that such a best extension exists and derive an algorithm for obtuning quch an extension. We also show that if instead we minimise the sum of (f(b)-,p[:?))2, th ere is generally a unique best extension, obtainable by solving a system of linear equa Lions.

📜 SIMILAR VOLUMES

A note on n-extendable graphs

✍ Qinglin Yu 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 249 KB

## Abstract A graph __G__ having a perfect matching is called n‐__extendable__ if every matching of size __n__ of __G__ can be extended to a perfect matching. In this note, we show that if __G__ is an __n__‐extendable nonbipartite graph, then __G__ + __e__ is (__n__ ‐ 1)‐extendable for any edge e ϵ

On a multiplicative graph function conje

On a multiplicative graph function conjecture

✍ Lih-Hsing Hsu 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 802 KB

For any graph H, the function h,. defined by setting h,(G) equal to the number of homomorphisms from G into H, is a multiplicative increasing function. L.ov&sz [2] has asked whether ail nonzero multiplicative increasing functions are generated by functions of this type. We show that this is not the

A Note on the Zeta Function of a Graph

✍ Sam Northshield 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 113 KB

The number of spanning trees in a finite graph is first expressed as the derivative (at 1) of a determinant and then in terms of a zeta function. This generalizes a result of Hashimoto to non-regular graphs. ## 1998 Academic Press Let G be a finite graph. The complexity of G, denoted }, is the num

On the Natural Imprint Function of a Gra

On the Natural Imprint Function of a Graph

✍ Boštjan Brešar 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 130 KB

In this paper, some characterizations of median and quasi-median graphs are extended to general isometric subgraphs of Cartesian products using the concept of an imprint function as introduced by Tardif. This extends the well known concepts of medians in median graphs as well as imprints in quasi-me

A result on extendibility in the powers

A result on extendibility in the powers of graphs

✍ Kara Walcher Shavo 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 309 KB

## Abstract Let __G__ be a graph on __p__ vertices. Then for a positive integer __n__, __G__ is said to be __n__‐extendible if (i) __n__ < __p__/2, (ii) __G__ has a set of __n__ independent edges, and (iii) every such set is contained in a perfect matching of __G__. The purpose of this article is t

On 2-extendable abelian Cayley graphs

✍ Onn Chan; C.C. Chen; Qinglin Yu 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 737 KB

A graph G is 2-extendable if any two independent edges of G are contained in a perfect matching of G. A Cayley graph of even order over an abelian group is 2-extendable if and only if it is not isomorphic to any of the following circulant graphs: (I) Z2.(1,2n -1), n >~ 3; (II) ZE.(1,2,2n -1,2n -2),