{"title":"Induced Acyclic Path Decomposition in Graphs","authors":"Abraham V. M., I. Sahul Hamid","country":null,"institution":"","volume":37,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":109,"pagesEnd":113,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/13","abstract":"A decomposition of a graph G is a collection \u03c8 of\r\ngraphs H1,H2, . . . , Hr of G such that every edge of G belongs\r\nto exactly one Hi. If each Hi is either an induced path in G,\r\nthen \u03c8 is called an induced acyclic path decomposition of G and\r\nif each Hi is a (induced) cycle in G then \u03c8 is called a (induced)\r\ncycle decomposition of G. The minimum cardinality of an induced\r\nacyclic path decomposition of G is called the induced acyclic path\r\ndecomposition number of G and is denoted by \u00a4\u00c7ia(G). Similarly\r\nthe cyclic decomposition number \u00a4\u00c7c(G) is defined. In this paper we\r\nbegin an investigation of these parameters.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 37, 2010"}