Detection number of bipartite graphs and cubic graphs

Frédéric Havet 1 Nagarajan Paramaguru 2 Rathinaswamy Sampathkumar 3
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : For a connected graph G of order |V(G)| ≥3 and a k-labelling c : E(G) →{1,2,…,k} of the edges of G, the code of a vertex v of G is the ordered k-tuple (ℓ1,ℓ2,…,ℓk), where ℓi is the number of edges incident with v that are labelled i. The k-labelling c is detectable if every two adjacent vertices of G have distinct codes. The minimum positive integer k for which G has a detectable k-labelling is the detection number det(G) of G. In this paper, we show that it is NP-complete to decide if the detection number of a cubic graph is 2. We also show that the detection number of every bipartite graph of minimum degree at least 3 is at most 2. Finally, we give some sufficient condition for a cubic graph to have detection number 3.
Document type :
Journal articles
Liste complète des métadonnées

Cited literature [12 references]  Display  Hide  Download

https://hal.inria.fr/hal-01110978
Contributor : Frederic Havet <>
Submitted on : Wednesday, November 4, 2015 - 2:39:57 PM
Last modification on : Monday, November 5, 2018 - 3:36:03 PM
Document(s) archivé(s) le : Friday, February 5, 2016 - 11:29:58 AM

File

dmtcs-16-3-20.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01110978, version 1

Collections

Citation

Frédéric Havet, Nagarajan Paramaguru, Rathinaswamy Sampathkumar. Detection number of bipartite graphs and cubic graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 3 (in progress) (3), pp.333-342. ⟨hal-01110978⟩

Share

Metrics

Record views

428

Files downloads

580