Characterization of signed paths and cycles admitting minus dominating function
نویسندگان
چکیده مقاله:
If G = (V, E, σ) is a finite signed graph, a function f : V → {−1, 0, 1} is a minusdominating function (MDF) of G if f(u) +summation over all vertices v∈N(u) of σ(uv)f(v) ≥ 1 for all u ∈ V . In this paper we characterize signed paths and cycles admitting an MDF.
منابع مشابه
Identifying codes and locating-dominating sets on paths and cycles
Let G = (V,E) be a graph and let r ≥ 1 be an integer. For a set D ⊆ V , define Nr[x] = {y ∈ V : d(x, y) ≤ r} and Dr(x) = Nr[x] ∩ D, where d(x, y) denotes the number of edges in any shortest path between x and y. D is known as an r-identifying code (r-locating-dominating set, respectively), if for all vertices x ∈ V (x ∈ V \D, respectively), Dr(x) are all nonempty and different. In this paper, w...
متن کاملShort Dominating Paths and Cycles in the Binary Hypercube
A sequence of binary words of length n is called a cube dominating path, if the Hamming distance between two consecutive words is always one, and every binary word of length n is within Hamming distance one from at least one of these words. If also the first and last words are Hamming distance one apart, the sequence is called a cube dominating cycle. Bounds on the cardinality of such sequences...
متن کاملConnected dominating set in graphs without long paths and cycles
The ratio of the connected domination number, γc, and the domination number, γ, is strictly bounded from above by 3. It was shown by Zverovich that for every connected (P5, C5)-free graph, γc = γ. In this paper, we investigate the interdependence of γ and γc in the class of (Pk, Ck)-free graphs, for k ≥ 6. We prove that for every connected (P6, C6)-free graph, γc ≤ γ+1 holds, and there is a fam...
متن کاملIndependent sets and independent dominating sets in the strong product of paths and cycles
In this paper we will consider independent sets and independent dominating sets in the strong product of two paths, two cycles and a path and a cycle.
متن کاملMinimum Degree and Dominating Paths
A dominating path in a graph is a path P such that every vertex outside P has a neighbor on P. A result of Broersma from 1988 implies that if G is an n-vertex k-connected graph and δ(G) > n−k k+2 − 1, then G contains a dominating path. We prove the following results. The lengths of dominating paths include all values from the shortest up to at least min{n − 1,2δ(G)}. For δ(G) > an, where a is a...
متن کاملthe common minimal dominating signed graph
in this paper, we define the common minimal dominating signed graph of a given signed graph and offer a structural characterization of common minimal dominating signed graphs. in the sequel, we also obtained switching equivalence characterizations: $overline{s} sim cmd(s)$ and $cmd(s) sim n(s)$, where $overline{s}$, $cmd(s)$ and $n(s)$ are complementary signed gra...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 5 شماره 1
صفحات 61- 68
تاریخ انتشار 2020-06-01
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023