Optimization Mode Research of Weighted Undirected Graph

Research on DNA Computing Methods of Optimization Problems on Weighted Graph

The paper researched the DNA computing method of classical optimization problems on weighted graph, improved the method of Weight-coding that belongs to the original model of DNA, raised some new methods of DNA encoding and DNA computing. Generally speaking, through the Relative length graph design that belongs to an Undirected weighted graph , given DNA coding and DNA computing a new method by...

dynamic coloring of graph

در این پایان نامه رنگ آمیزی دینامیکی یک گراف را بیان و مطالعه می کنیم. یک –kرنگ آمیزی سره ی رأسی گراف g را رنگ آمیزی دینامیکی می نامند اگر در همسایه های هر رأس v?v(g) با درجه ی حداقل 2، حداقل 2 رنگ متفاوت ظاهر شوند. کوچکترین عدد صحیح k، به طوری که g دارای –kرنگ آمیزی دینامیکی باشد را عدد رنگی دینامیکی g می نامند و آنرا با نماد ?_2 (g) نمایش می دهند. مونت گمری حدس زده است که تمام گراف های منتظم ...

The Main Eigenvalues of the Undirected Power Graph of a Group

The undirected power graph of a finite group $G$, $P(G)$, is a graph with the group elements of $G$ as vertices and two vertices are adjacent if and only if one of them is a power of the other. Let $A$ be an adjacency matrix of $P(G)$. An eigenvalue $lambda$ of $A$ is a main eigenvalue if the eigenspace $epsilon(lambda)$ has an eigenvector $X$ such that $X^{t}jjneq 0$, where $jj$ is the all-one...

Parallel Strong Orientation of an Undirected Graph

Effective All-Pairs Dijkstra’s Algorithm for Computing Undirected Weighted Graph Metrics

The graph metric of an undirected graph can be represented by a symmetric matrix in which each entry is the graph distance between the corresponding nodes, i.e., the shortest path distance between them. This article presents an improved all-pairs Dijkstra’s algorithm for computing the graph metric on an undirected weighted graph. Taking the advantage of the symmetric property of the graph metri...