SOME NEW FAMILY OF GRACEFUL LOBSTERS.
The lobsters with central paths H= X< sub> 0, x< sub> 1,..., x< sub> m to which we give
graceful labelings satisfy the following properties:(i) The vertex X< sub> 0 may be attached
to one among the combinations (e, o, e),(e, e, o),(0, o, e) and (0, e, o).(ii) The path H\{X<
sub> 0} can be partitioned into subpaths p< sub> i, 1≤ i≤ k with the following properties:(a)
P< sub> i consists of at most four vertices.(b) Each vertex in P< sub> i is attached to an odd
(or even) number of branches. If each vertex in p< sub> i is attached to an odd number of …
graceful labelings satisfy the following properties:(i) The vertex X< sub> 0 may be attached
to one among the combinations (e, o, e),(e, e, o),(0, o, e) and (0, e, o).(ii) The path H\{X<
sub> 0} can be partitioned into subpaths p< sub> i, 1≤ i≤ k with the following properties:(a)
P< sub> i consists of at most four vertices.(b) Each vertex in P< sub> i is attached to an odd
(or even) number of branches. If each vertex in p< sub> i is attached to an odd number of …
Abstract
The lobsters with central paths H= X0, x1,..., xm to which we give graceful labelings satisfy the following properties:(i) The vertex X0 may be attached to one among the combinations (e, o, e),(e, e, o),(0, o, e) and (0, e, o).(ii) The path H\{X0} can be partitioned into subpaths pi, 1≤ i≤ k with the following properties:(a) Pi consists of at most four vertices.(b) Each vertex in Pi is attached to an odd (or even) number of branches. If each vertex in pi is attached to an odd number of branches, then the length of Pi is 4.
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