L(d,1)-labellings of generalised Petersen graphs
by Fei Deng; Xiaoling Zhong; Zehui Shao
International Journal of Autonomous and Adaptive Communications Systems (IJAACS), Vol. 11, No. 2, 2018

Abstract: An interesting graph distance constrained labelling problem can model the frequency channel assignment problem as well as code assignment in computer networks. The frequency assignment problem asks for assigning frequencies to transmitters in a broadcasting network with the aim of avoiding undesired interference. One of the graph theoretical models of The frequency assignment problem is the concept of distance constrained labelling of graphs. Let u and v be vertices of a graph G = (V (G),E(G)) and d(u, v) be the distance between u and v in G. For an integer d ≥ 0, an L(d, 1)-labelling of G is a function f : V (G) → {0, 1, · · · } such that for every u, vV (G), |f(u) − f(v)| ≥ d if d(u, v) = 1 and |f(u) − f(v)| ≥ 1 if d(u, v) = 2. The span of f is the difference between the largest and the smallest numbers in f(V (G)). The λd,1-number of G is the minimum span over all L(d, 1)-labellings of G. For natural numbers n and k, where n > 2k, a generalised Petersen graph P(n, k) is obtained by letting its vertex set be {u1, u2, · · · , un} ∪ {v1, v2, · · · , vn} and its edge set be the union of uiui+1, uivi, vivi+k over 1 ≤ in, where subscripts are reduced modulo n. In this paper, we show the λd,1-numbers of the generalised Petersen graphs P(n, k) for n ≥ 5.

Online publication date: Wed, 30-May-2018

The full text of this article is only available to individual subscribers or to users at subscribing institutions.

Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.

Pay per view:
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.

Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Autonomous and Adaptive Communications Systems (IJAACS):
Login with your Inderscience username and password:

    Username:        Password:         

Forgotten your password?

Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.

If you still need assistance, please email subs@inderscience.com