منابع مشابه
On the total edge irregularity strength of hexagonal grid graphs
An edge irregular total k-labeling of a graph G = (V,E) is a labeling φ : V ∪ E → {1, 2, . . . , k} such that the total edge-weights wt(xy) = φ(x) + φ(xy) + φ(y) are different for all pairs of distinct edges. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G. In this paper, we determined the exact values of the total e...
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It is an elementary exercise to show that any non-trivial simple graph has two vertices with the same degree. This is not the case for digraphs and multigraphs. We consider generating irregular digraphs from arbitrary digraphs by adding multiple arcs. To this end, we define an irregular labeling of a digraph D to be an arc labeling of the digraph such that the ordered pairs of the sums of the i...
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On graph irregularity strength
An assignment of positive integer weights to the edges of a simple graph G is called irregular, if the weighted degrees of the vertices are all different. The irregularity strength, s(G), is the maximal weight, minimized over all irregular assignments. In this study, we show that s(G) c1 n / , for graphs with maximum degree n and minimum
متن کاملIrregularity strength of dense graphs
Let G be a simple graph of order n with no isolated vertices and no isolated edges. For a positive integer w, an assignment f on G is a function f : E(G) → {1, 2, . . . , w}. For a vertex v, f(v) is defined as the sum f(e) over all edges e of G incident with v. f is called irregular, if all f(v) are distinct. The smallest w for which there exists an irregular assignment on G is called the irreg...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00207-5