The zero divisor graph of a commutative ring is a graph whose vertices are non-zero zero divisors of and two vertices are adjacent if their product is zero. The characteristic polynomial of matrix is defined as and roots ...

If for any total dominating set D with v∈V(G) - D there exists a vertex u ∈ D such that uv∈E(G) and |d(v) - d(u)|≤ 1 then D is called the total equitable dominating set. The minimum cardinality of the total equitable ...