WebIn this paper, we introduce a new kind of graph energy, the minimum edge covering energy, ECE ( G ). It depends both on the underlying graph G, and on its particular minimum edge covering CE. Upper and lower bounds for ECE ( G) are established. WebLet G be a graph on n vertices and m edges, with maximum degree Δ(G) and minimum degree δ(G). Let A be the adjacency matrix of G, and let λ1≥λ2≥…≥λn be the …

graph theory - Maximum size of a minimal vertex cover

Web24 mrt. 2024 · The vertex set of a graph is therefore always a vertex cover. The smallest possible vertex cover for a given graph is known as a minimum vertex cover (Skiena 1990, p. 218), and its size is called the vertex cover number, denoted . Vertex covers, indicated with red coloring, are shown above for a number of graphs. Web20 okt. 2010 · Convert your input graph G (V, E) to a weighted graph G' (N, D), where N is the subset of vertices you want to cover and D is distances (path lengths) between corresponding vertices in the original graph. This will "collapse" all vertices you don't need into edges. Compute the minimum spanning tree for G'. chris schwarz tool chest plans

8.5: Potential Energy Diagrams and Stability - Physics LibreTexts

WebMinimum Line Covering. It is also known as Smallest Minimal Line Covering. A minimal line covering with minimum number of edges is called a minimum line covering of ‘G’. … Web1 jan. 2015 · Abstract In this paper, we introduced the concept of minimum covering color energy ECc (G) of a graph G and computed minimum covering chromatic energies of … Web15 jun. 2010 · Consider the following undirected graph: The set of vertices {2,4,5} is a minimum vertex cover of the graph. Why? because it's a vertex cover (all edges are covered) and there is no other vertex cover with fewer vertices. The set of vertices {2,3,5,6,7} is a minimal vertex cover. chris stockwell