Vol. 29, No. 3, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Eigenvalues of the adjacency matrix of cubic lattice graphs

Renu Chakravarti Laskar

Vol. 29 (1969), No. 3, 623–629
Abstract

A cubic lattice graph is defined to be a graph G, whose vertices are the ordered triplets on n symbols, such that two vertices are adjacent if and only if they have two coordinates in common. If n2(x) denotes the number of vertices y, which are at distance 2 from x and A(G) denotes the adjacency matrix of G, then G has the following properties: (P1) the number of vertices is n3. (P2) G is connected and regular. (P3) n2(x) = 3(n 1)2. (P4) the distinct eigenvalues of A(G) are 3, n 3, 2n 3, 3(n 1). It is shown here that if n > 7, any graph G (with no loops and multiple edges) having the properties (P1)–(P4) must be a cubic lattice graph. An alternative characterization of cubic lattice graphs has been given by the author (J. Comb. Theory, Vol. 3, No. 4, December 1967, 386–401).

Mathematical Subject Classification
Primary: 05.40
Milestones
Received: 10 May 1968
Published: 1 June 1969
Authors
Renu Chakravarti Laskar