Distance-two labelings of graphs
نویسندگان
چکیده
For given positive integers j ≥ k, an L( j, k)-labeling of a graph G is a function f : V (G) → {0, 1, 2, . . .} such that | f (u) − f (v)| ≥ j when dG (u, v) = 1 and | f (u) − f (v)| ≥ k when dG (u, v) = 2. The L( j, k)-labeling number λ j,k(G) of G is defined as the minimum m such that there is an L( j, k)-labeling f of G with f (V (G)) ⊆ {0, 1, 2, . . . ,m}. For a graph G of maximum degree ∆ ≥ 1 it is the case that λ j,k(G) ≥ j + (∆− 1)k. The purpose of this paper is to study the structures of graphs G with maximum degree ∆ ≥ 1 and λ j,k(G) = j + (∆ − 1)k. c © 2003 Elsevier Science Ltd. All rights reserved.
منابع مشابه
Constructions of antimagic labelings for some families of regular graphs
In this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.
متن کاملExact Distance Labelings Yield Additive-Stretch Compact Routing Schemes
Distance labelings and compact routing schemes have both been active areas of recent research. It was already known that graphs with constant-sized recursive separators, such as trees, outerplanar graphs, series-parallel graphs and graphs of bounded treewidth, support both exact distance labelings and optimal (additive stretch 0, multiplicative stretch 1) compact routing schemes, but there are ...
متن کاملBalanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations
A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...
متن کاملSnakes and Caterpillars in Graceful Graphs
Graceful labelings use a prominent place among difference vertex labelings. In this work we present new families of graceful graphs all of them obtained applying a general substitution result. This substitution is applied here to replace some paths with some trees with a more complex structures. Two caterpillars with the same size are said to be textit{analogous} if thelarger stable sets, in bo...
متن کاملRadio labelings of distance graphs
for any two distinct vertices x and y, where d(x, y) is the distance between x and y in G. The radio k-labeling number rlk(G) of G is the minimum of maxx,y∈V (G) |f(x)− f(y)| over all radio k-labelings f of G. The study of radio k-labelings was initiated by Chartrand et al. [1], motivated by radio channel assignment problems with interference constraints. Except for paths [1, 3] and cycles [5],...
متن کاملGraceful labelings of the generalized Petersen graphs
A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 24 شماره
صفحات -
تاریخ انتشار 2003