On graph irregularity strength

نویسندگان

  • Alan M. Frieze
  • Ronald J. Gould
  • Michal Karonski
  • Florian Pfender
چکیده

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

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Total vertex irregularity strength of corona product of some graphs

A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the to...

متن کامل

On Total Edge Irregularity Strength of Staircase Graphs and Related Graphs

Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G ...

متن کامل

Total Edge Irregularity Strength of Strong Product of Cycles and Paths

An irregular assignment is a k -labeling of the edges : {1, 2, , } f E k → ... such that the vertex weights (label sums of edges incident with the vertex) are different for all vertices of G . The smallest k for which there is an irregular assignment is the irregularity strength. The notion of irregularity strength was introduced by Chartrand et al. [8] and studied by numerous authors, see [6,1...

متن کامل

On edge irregularity strength of subdivision of star Sn

In this paper, we study the total edge irregularity strength of some well known graphs. An edge irregular total k-labeling φ : V ∪E → {1, 2, . . . , k} of a graph G = (V,E) is a labeling of vertices and edges of G in such a way that for any different edges xy and x′y′ their weights are distinct. The total edge irregularity strength tes(G) is defined as the minimum k for which G has an edge irre...

متن کامل

On the irregularity strength of trees

For any graph G, let ni be the number of vertices of degree i, and λ(G) = maxi≤j{ ni+···+nj+i−1 j }. This is a general lower bound on the irregularity strength of graph G. All known facts suggest that for connected graphs, this is the actual irregularity strength up to an additive constant. In fact, this was conjectured to be the truth for regular graphs and for trees. Here we find an infinite ...

متن کامل

On total edge irregularity strength of categorical product of cycle and path

We investigate a modification of well known irregularity strength of graph, namely the total edge irregularity strength. An edge irregular total k-labeling φ : V ∪E → {1, 2, . . . , k} of a graph G is a labeling of vertices and edges of G in such a way that for any two different edges uv and u′v′ their weights φ(u)+φ(uv)+φ(v) and φ(u′)+φ(u′v′)+φ(v′) are distinct. The total edge irregularity str...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Journal of Graph Theory

دوره 41  شماره 

صفحات  -

تاریخ انتشار 2002