A degree condition for the existence of connected factors

A Degree Condition For Graphs to Have Connected (g, f)-Factors

On the edge-connectivity of C_4-free graphs

Let $G$ be a connected graph of order $n$ and minimum degree $delta(G)$.The edge-connectivity $lambda(G)$ of $G$ is the minimum numberof edges whose removal renders $G$ disconnected. It is well-known that$lambda(G) leq delta(G)$,and if $lambda(G)=delta(G)$, then$G$ is said to be maximally edge-connected. A classical resultby Chartrand gives the sufficient condition $delta(G) geq frac{n-1}{2}$fo...

Design of A Single-Phase Transformerless Grid-Connected PV Inverter ‎Considering Reduced Leakage Current and LVRT Grid Codes

A new single-phase transformerless grid-connected PV inverter is presented in this paper. Investigations in transformerless grid-connected PV inverters indicate the existence of the leakage current is directly related to the variable common-mode voltage (CMV), which is presented in detail. On the other hand, in recent years it has become mandatory for the transformerless grid-connected PV inver...

Sufficient conditions on the zeroth-order general Randic index for maximally edge-connected digraphs

Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree  and its in-degree . Now let D be a digraph with minimum degree  and edge-connectivity If  is real number, then the zeroth-order general Randic index is defined by   .  A digraph is maximally edge-connected if . In this paper we present sufficient condi...

2- and 3-factors of Graphs on Surfaces

It has been conjectured that any 5-connected graph embedded in a surface Σ with sufficiently large face-width is hamiltonian. This conjecture was verified by Yu for the triangulation case, but it is still open in general. The conjecture is not true for 4-connected graphs. In this paper, we shall study the existence of 2and 3-factors in a graph embedded in a surface Σ. A hamiltonian cycle is a s...