Induced Graphoidal Covers in a Graph

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

Abstract:

An induced graphoidal cover of a graph G is a collection ψ of (not necessarily open) paths in G such that every path in ψ has at least 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 cycle or an induced path. The minimum cardinality of an induced graphoidal cover of G is called the induced graphoidal covering number of G and is denoted by ηi(G) or ηi. Here we find induced graphoidal cover for some classes of graphs.

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

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1074940

References:

[1] B. D. Acharya, E. Sampathkumar, Graphoidal covers and graphoidal covering number of a graph, Indian J. Pure Appl. Math., 18 (10) (1987) pp 882-890.
[2] S. Arumugam, S, Hamid, Simple graphoidal covers in a graph, J. Comb. Math. Comb. Comput., 64 (2008) pp 79-95 .
[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, pp 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 3-7, 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).