There are many different mathematical objects (transitive reductions, minimal equivalent digraphs, minimal connected graphs, Hasse diagrams and so on) that are defined on graphs. Although they have different names they correspond to the same object if a weighted graph is defined more generally. The
The energy change of weighted graphs
β Scribed by Ivan Gutman; Jia-Yu Shao
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 192 KB
- Volume
- 435
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
Let (G, w ) denote a simple graph G with a weight function w : β¬(G) -{0,1,2}. A path cover of (G, w ) is a collection of paths in G such that every edge e is contained in exactly w(e) paths of the collection. For a vertex u , w ( v ) is the sum of the weights of the edges incident with U ; U is call
Suppose that G is a finite simple graph and w is a weight function which assigns to each vertex of G a nonnegative real number. Let C be a circle of length t . A t-circular coloring of (G,w) is a mapping A of the vertices of G to arcs of C such that A(%) n A(y) = 0 if (x, y) E E ( G ) and A(x) has l
## Abstract Suppose __G__ is a graph, __k__ is a nonβnegative integer. We say __G__ is __k__βantimagic if there is an injection __f__: __E__β{1, 2, β¦, |__E__| + __k__} such that for any two distinct vertices __u__ and __v__, . We say __G__ is weightedβ__k__βantimagic if for any vertex weight functi
## Abstract The notion of (circular) colorings of edgeβweighted graphs is introduced. This notion generalizes the notion of (circular) colorings of graphs, the channel assignment problem, and several other optimization problems. For instance, its restriction to colorings of weighted complete graphs