{"title":"Induced Acyclic Graphoidal Covers in a Graph","authors":"K. Ratan Singh, P. K. Das","volume":44,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1078,"pagesEnd":1085,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/11912","abstract":"An induced acyclic graphoidal cover of a graph G is a\r\ncollection \u03c8 of open paths in G such that every path in \u03c8 has atleast\r\ntwo vertices, every vertex of G is an internal vertex of at most one\r\npath in \u03c8, every edge of G is in exactly one path in \u03c8 and every\r\nmember of \u03c8 is an induced path. The minimum cardinality of an\r\ninduced acyclic graphoidal cover of G is called the induced acyclic\r\ngraphoidal covering number of G and is denoted by \u03b7ia(G) or \u03b7ia.\r\nHere we find induced acyclic graphoidal cover for some classes of\r\ngraphs.","references":"[1] B. D. Acharya, E. Sampathkumar, Graphoidal covers and graphoidal\r\ncovering number of a graph, Indian J. Pure Appl. Math. 18 (10) (1987)\r\n882-890.\r\n[2] S. Arumugam, J. Suresh Suseela, Acyclic graphoidal covers and path\r\npartitins in a graph, Discrete Math., 190 (1998) 67-77 .\r\n[3] S. Arumugam, B. D. Acharya, E. Sampathkumar, Graphoidal covers of\r\na graph: a creative review, in Proc. National Workshop on Graph Theory\r\nand its applications, Manonmaniam Sundaranar University, Tirunelveli,\r\nTata McGraw-Hill, New Delhi 1-28 1997.\r\n[4] S. Arumugam, Path covers in graphs, Lecture Notes of the National\r\nWorkshop on Decompositions of Graphs and Product Graphs held at\r\nAnnamalai University, Tamil Nadu, during January 37, 2006.\r\n[5] F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.\r\n[6] K. Ratan Singh, P. K. Das, On graphoidal covers of bicyclic graphs,\r\n(submitted for publication).\r\n[7] K. Ratan Singh, P. K. Das, Induced Graphoidal Covers in a Graph, Int.\r\nJ. of Mathematical and Statistical Sciences, 2 (3) (2010) 102-106.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 44, 2010"}