On the broadcast independence number of caterpillars
نویسندگان
چکیده
منابع مشابه
On the Broadcast Independence Number of Caterpillars
Let G be a simple undirected graph. A broadcast on G is a function f : V (G) → N such that f(v) ≤ eG(v) holds for every vertex v of G, where eG(v) denotes the eccentricity of v in G, that is, the maximum distance from v to any other vertex of G. The cost of f is the value cost(f) = ∑ v∈V (G) f(v). A broadcast f on G is independent if for every two distinct vertices u and v in G, dG(u, v) > max{...
متن کاملGirth, minimum degree, independence, and broadcast independence
An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...
متن کاملThe number of caterpillars
A caterpillar is a tree which metamorphoses into a path when its cocoon of endpoInt\ is removed. The number of nonisomorphic caterpillars with n + 4 points is 2n + 2 [n/21 . This neat formula is proved in two ways: first, as a special caoe of an application of Pblya’s enumerration theorem which counts graphs with integer-weightell points; secondly, 3y an appropriate labeling of the lines of the...
متن کاملUnimodality of the independence polynomials of non-regular caterpillars
The independence polynomial I(G, x) of a graph G is the polynomial in variable x in which the coefficient an on x n gives the number of independent subsets S ⊆ V (G) of vertices of G such that |S| = n. I(G, x) is unimodal if there is an index μ such that a0 ≤ a1 ≤ · · · ≤ aμ−1 ≤ aμ ≥ aμ+1 ≥ · · · ≥ ad−1 ≥ ad. While the independence polynomials of many families of graphs with highly regular stru...
متن کاملThe Game Chromatic Number of 1-Caterpillars
The game chromatic number of a graph is defined using a two players game. In 1993, Faigle et al. proved that the game chromatic number of trees is at most four. In this paper we investigate the problem of characterizing those trees with game chromatic number three, and setttle this problem for 1-caterpillars.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2018
ISSN: 0166-218X
DOI: 10.1016/j.dam.2018.03.017