The edge clique cover number ecc(G) of a graph G is the size of the smallest collection of complete subgraphs whose union covers all edges of G. Chen, Jacobson, Kézdy, Lehel, Scheinerman, and Wang conjectured in 2000 that if G is claw‐free, then ecc(G) is bounded above by...
Minimum weight edge covering problem, known as a classic problem in graph theory, is employed in many scientific and engineering applications. In the applications, the weight may denote cost, time, or opponent's payoff, which can be vague in practice. This paper considers the edge covering ...
Let G be a fixed graph with largest (adjacency matrix) eigenvalue lambda(0) and with its universal cover having spectral radius p. W show that a random cov... Friedman,Joel - 《Duke Mathematical Journal》 被引量: 103发表: 2003年 Random Lifts of Graphs: Edge Expansion We continue the st...
value attains the minimum among all graphs of a fixed order and a given vertex (edge) independence number or vertex (edge) cover number, and get some bounds for the vertex (edge) independence number, vertex (edge) cover number of a graph in terms of the least eigenvalue of the graph....
In this note we show how to compute the spectrum of G by computing the spectrum of two smaller graphs, namely a (modified) form of the covered graph H and another graph which we term the anti-cover. This is done for both the adjacency matrix and the normalized Laplacian. We also give...
value attains the minimum among all graphs of a fixed order and a given vertex (edge) independence number or vertex (edge) cover number, and get some bounds for the vertex (edge) independence number, vertex (edge) cover number of a graph in terms of the least eigenvalue of the graph....
Further, we also provide a framework, which is shown to compute the exact value of the cover time for a general family of stochastically-evolving graphs in exponential time. Finally, we conduct experiments on the cover time of \emph{RWA} in Edge-Uniform graphs and compare the experimental ...
producing confluent drawings automatically has proven quite difficult. We introduce the biclique edge cover graph that represents a graphGas an interconnected set of cliques and bicliques. We do this in such a way as to permit a straightforward transformation to a confluent drawing ofG. Our result...
[20]J. Širáň, T. W. Tucker and M. E. Watkins, Realizing finite edge-transitive orientable maps, J. Graph Theory 37 (2001), no. 1, 1–34.10.1002/jgt.1000.absSearch in Google Scholar [21]S. Wilson, Edge-transitive maps and non-orientable surfaces, Math. Slovaca 47 (1997), ...
8.1 Graph Theory Prerequisite: Section 1.5, Matrix Multiplication Multiplication of matrices is widely used in graph theory, a branch of mathematics that has come into prominence for modeling many situations in computer science, business, and the social sciences. We begin by introducing graphs and di...