Asian Basic and Applied Research Journal

On Full Friendly Index Sets of Generalized Petersen Graphs P(n, 2)

Kh. Md. Mominul Haque *

Department of Computer Science and Engineering, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh.

Umme Nasreen Khanam

Department of Computer Science, Jayntapur Tayob Ali Technical College, Jayntapur, Sylhet, Bangladesh.

*Author to whom correspondence should be addressed.

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Abstract

Suppose G = (V,E) be a connected graph. A vertex labeling f : V → \(\mathbb{Z}_2\) initiates a edge labeling f* : E → \(\mathbb{Z}_2\) described by f* (xy) = f(x) + f(y) for each xy \(\epsilon\) E. For i \(\epsilon\) \(\mathbb{Z}_2\), let vf (i) = |f^-1(i)| and ef (i) = |f^*-1(i)|. A labeling f is called friendly if |v_f (1) − v_f (0)| \(\leqslant\) 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by i_f (G) = ef (1) − e_f (0). The set of {i_f (G)| f is a friendly labeling of G} is called full friendly index set of G denoted by FFI(G). In this paper, we study the full friendly index sets of generalized Petersen graphs P(n, 2).

Keywords: Colchiploidy, Friendly index set, Breeding Vigna, friendly labeling, generalized Petersen graphs P(n; 2)

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