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Induced Acyclic Graphoidal Covers in a Graph

Authors: K. Ratan Singh, P. K. Das

Abstract:

An induced acyclic graphoidal cover of a graph G is a collection ψ of open paths in G such that every path in ψ has atleast two vertices, every vertex of G is an internal vertex of at most one path in ψ, every edge of G is in exactly one path in ψ and every member of ψ is an induced path. The minimum cardinality of an induced acyclic graphoidal cover of G is called the induced acyclic graphoidal covering number of G and is denoted by ηia(G) or ηia. Here we find induced acyclic graphoidal cover for some classes of graphs.

Keywords: Graphoidal cover, Induced acyclic graphoidal cover, Induced acyclic graphoidal covering number.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078172

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References:


[1] B. D. Acharya, E. Sampathkumar, Graphoidal covers and graphoidal covering number of a graph, Indian J. Pure Appl. Math. 18 (10) (1987) 882-890.
[2] S. Arumugam, J. Suresh Suseela, Acyclic graphoidal covers and path partitins in a graph, Discrete Math., 190 (1998) 67-77 .
[3] S. Arumugam, B. D. Acharya, E. Sampathkumar, Graphoidal covers of a graph: a creative review, in Proc. National Workshop on Graph Theory and its applications, Manonmaniam Sundaranar University, Tirunelveli, Tata McGraw-Hill, New Delhi 1-28 1997.
[4] S. Arumugam, 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 37, 2006.
[5] F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.
[6] K. Ratan Singh, P. K. Das, On graphoidal covers of bicyclic graphs, (submitted for publication).
[7] K. Ratan Singh, P. K. Das, Induced Graphoidal Covers in a Graph, Int. J. of Mathematical and Statistical Sciences, 2 (3) (2010) 102-106.