New Bounds of Induced Acyclic Graphoidal Decomposition Number of a Graph
- 376 Downloads
An induced acyclic graphoidal decomposition (IAGD) of a graph G is a collection ψ of nontrivial induced paths in G such that every edge of G lies in exactly one path of ψ and no two paths in ψ have a common internal vertex. The minimum cardinality of an IAGD of G is called the induced acyclic graphoidal decomposition number denoted by ηia(G). In this paper we present bounds for ηia(G) in terms of cut vertices and simplicial vertices of G.
- 1.Acharya, B. D., Sampathkumar, E.: Graphoidal covers and graphoidal covering number of a graph. Indian J.pure appl.Math. 18(10), 882–890 (1987)Google Scholar
- 2.Arumugam, S.: Path covers in graphs. Lecture Notes of the National Workshop on Decompositions of Graphs and Product Graphs held at Annamalai University, Tamil Nadu, during January 3–7, (2006)Google Scholar
- 7.Singh, K. R., Das, P. K.: Induced acyclic graphoidal covers in a graph. World Academy of Science, Engineering and Technology. 68, 38–44 (2010)Google Scholar
- 9.Hamid, I. S., Joseph, M: Decomposing graphs into internally-disjoint induced paths. SCIENTIA. Series A: Mathematical Sciences. 27 47–57(2016)Google Scholar
- 10.Stanton, R. G., Cowan, D. D., James, L.O.: Some results on path numbers. Proc. Louisiana Conf. on Combinatorics.Graph Theory and Computing, 112–135 (1970)Google Scholar