Let G be a graph of order n. For every v ∈ V (G), let EG(v) denote the set of all edges incident with v. A signed k-submatching of G is a function f : E(G) −→ {−1, 1}, satisfying f(EG(v)) ≤ 1 for at least k vertices, where f(S) = ∑ e∈S f(e), for each S ⊆ E(G). The maximum of the value of f(E(G)), taken over all signed k-submatching f of G, is called the signed k-submatching number and is denote...

A graph G is signed if each edge is assigned + or −. A signed graph is balanced if there is a bipartition of its vertex set such that an edge has sign − if and only if its endpoints are in different parts. The Edwards-Erdös bound states that every graph with n vertices and m edges has a balanced subgraph with at least m 2 +n−1 4 edges. In the Signed Max Cut Above Tight Lower Bound (Signed Max C...

A double Roman dominating function on a graph G=(V,E) is f:V?{0,1,2,3} with the properties that if f(u)=0, then vertex u adjacent to at least one assigned 3 or two vertices 2, and f(u)=1, 2 3. The weight of f equals w(f)=?v?Vf(v). domination number ?dR(G) G minimum G. said be ?dR(G)=3?(G), where ?(G) We obtain sharp lower bound generalized Petersen graphs P(3k,k), we construct solutions providi...

3 A function f : V (G) → {+1,−1} defined on the vertices of a graph G is a signed domi4 nating function if for any vertex v the sum of function values over its closed neighborhood 5 is at least one. The signed domination number γs(G) of G is the minimum weight of a 6 signed dominating function on G. By simply changing “{+1,−1}” in the above definition 7 to “{+1, 0,−1}”, we can define the minus ...

A graph G is signed if each edge is assigned + or −. A signed graph is balanced if there is a bipartition of its vertex set such that an edge has sign − if and only if its endpoints are in different parts. The Edwards-Erdös bound states that every graph with n vertices and m edges has a balanced subgraph with at least m 2 +n−1 4 edges. In the Signed Max Cut Above Tight Lower Bound (Signed Max C...

A recently proposed technique for common-multiplicand multiplication of binary numbers is shown to be applicable to signed-digit numbers. We prove that multiplication of a single k-bit multiplicand by n k-bit multipliers can be performed using 0:306nk additions for canonically recoded signed-digit numbers, while the binary case requires 0:375nk additions.