IJPAM: Volume 72, No. 2 (2011)

ON 2-GRAPHOIDAL COVERING NUMBER OF A GRAPH

P.K. Das$^1$, K. Ratan Singh$^2$
$^{1,2}$Department of Mathematics
NERIST
Arunachal Pradesh, 791 109, INDIA


Abstract. A 2-graphoidal cover of a graph $G$ is a collection $\psi$ of paths (not necessarily open) in $G$ such that every path in $\psi$ has at least two vertices, every vertex of $G$ is an internal vertex of at most two paths in $\psi$ and every edge of $G$ is in exactly one path in $\psi$. The minimum cardinality of a 2-graphoidal cover of $G$ is called the 2-graphoidal covering number of $G$ and is denoted by $\eta_2(G)$ or $\eta_2$. Here, we study 2-graphoidal covering number for some classes of graphs.

Received: February 9, 2011

AMS Subject Classification: 05C70

Key Words and Phrases: graphoidal cover, 2-graphoidal cover, 2-graphoidal covering number

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 72
Issue: 2