Discrete Mathematics - Special issue: advances in graph labelling
Discrete Mathematics
Some results on the achromatic number
Journal of Graph Theory
The computational complexity of cordial and equitable labelling
Discrete Mathematics
New spectral methods for ratio cut partitioning and clustering
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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Let G=(V,E) be a graph, a vertex labeling f:V-Z"2 induces an edge labeling f^*:E-Z"2 defined by f^*(xy)=f(x)+f(y) for each xy@?E. For each, i@?Z"2 define v"f(i)=|f^-^1(i)| and e"f(i)=|f^*^-^1(i)|. We call f friendly if |v"f(1)-v"f(0)|@?1. The full friendly index set of G is the set of all possible values of e"f(1)-e"f(0), where f is friendly. In this paper, we study the full friendly index sets of some standard graphs such as the complete graph K"n, the cycle C"n, fans F"m and F"2","m and the Cartesian product of P"3 and P"n i.e. P"3xP"n.