ON GRACEFUL AND CORDIAL LABELING OF SHELL GRAPHS

We recall from [13] a shell graph of size n, denoted C(n, n-3), is the graph obtained from the cycle C-n < v(0), v(1), v(2),...,v(n-1)> by adding n-3 consecutive chords incident at a common vertex, say v(0). The vertex v(0) of C(n, n-3) is called apex of the shell C(n, n-3). The vertex v(1) of C(n, n-3) is said to be at level 1. A graph C(2n, n-2) is called an alternate shell, if C(2n, n-2) is obtained from the cycle C-2n < v(0), v(1), v(2),...,v(2n-1)> by adding n-2 chords between the vertex v(0) and the vertices v(2)i(+1), for 1 <= i <= n-2. If the vertex v(1) of C(2n, n-2) at level 1 and is adjacent with v(0) then v(1) is said to be at level 1 with a chord otherwise the vertex v(1) is said to be at level 1 without a chord