Induced Acyclic Path Decomposition in Graphs

Authors: Abraham V. M., I. Sahul Hamid

Abstract:

A decomposition of a graph G is a collection ψ of graphs H1,H2, . . . , Hr of G such that every edge of G belongs to exactly one Hi. If each Hi is either an induced path in G, then ψ is called an induced acyclic path decomposition of G and if each Hi is a (induced) cycle in G then ψ is called a (induced) cycle decomposition of G. The minimum cardinality of an induced acyclic path decomposition of G is called the induced acyclic path decomposition number of G and is denoted by ¤Çia(G). Similarly the cyclic decomposition number ¤Çc(G) is defined. In this paper we begin an investigation of these parameters.

Keywords: Cycle decomposition, Induced acyclic path decomposition, Induced acyclic path decomposition number.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1327466

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