On Odd Arithmetic Graphs

Abstract:

      The following results are obtained: (1) The graph $C^n_m\cdot P_t$ is odd arithmetic when (i) $m\equiv 0$ (mod 2) and $t$=$m$ or$m+1$; (ii) $m\equiv 1$ (mod 2) and $t$=$m+1$. (2) The graph$C^n_{2m}$ is odd arithmetic when (i) $m$=2,4 and $n$ is any positive integer; (ii) $m$=3 and $n$ is even. (3) The graph $C_{m}^n$ is odd arithmetic when $m$=$4n$ and $t$=2. (4) $P_{m+1}^n$ is odd arithmetic when (i) $n$ is odd; (ii) $m\leq 3$ and $n$ is any positive integer. (5) Windmill graph $K_n^t$ is odd arithmetic if and only if $n$=2. (6) Cycle $C_n$ is odd arithmetic if and only if $n\equiv 0$ (mod 4). (7) For any positive integer $n$ and any positive integer $m$, $K_{m,n}$ is odd arithmetic.