A degree sum condition for the existence of a path-factor

Balanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

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

Designing Path for Robot Arm Extensions Series with the Aim of Avoiding Obstruction with Recurring Neural Network

In this paper, recurrent neural network is used for path planning in the joint space of the robot with obstacle in the workspace of the robot. To design the neural network, first a performance index has been defined as sum of square of error tracking of final executor. Then, obstacle avoidance scheme is presented based on its space coordinate and its minimum distance between the obstacle and ea...

Shortest Path Problem with Gamma Probability Distribution Arc Length

We propose a dynamic program to find the shortest path in a network having gamma probability distributions as arc lengths. Two operators of sum and comparison need to be adapted for the proposed dynamic program. Convolution approach is used to sum two gamma probability distributions being employed in the dynamic program.

MORE GRAPHS WHOSE ENERGY EXCEEDS THE NUMBER OF VERTICES

The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of G. Several classes of graphs are known that satisfy the condition E(G) > n , where n is the number of vertices. We now show that the same property holds for (i) biregular graphs of degree a b , with q quadrangles, if q<= abn/4 and 5<=a < b = 0 (iii) triregular graphs of degree 1, a, b that are quadran...