Uniformly optimally reliable graphs: A survey

نویسندگان

چکیده

Which is the most reliable graph with n nodes and m edges? This celebrated problem has several aspects, according to notion of optimality (in a local or uniform sense), failure type (either edges), reliability model (all-terminal connectedness, two-terminal multiterminal setting). article presents chronological survey multiple proposals address problem, together recent trends enigmatic conjectures posed decades ago that promote further research.

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Note on Selling Optimally Two Uniformly Distributed Goods

We provide a new, much simplified and straightforward proof to a result of Pavlov [2011] regarding the revenue maximizing mechanism for selling two items with uniformly i.i.d. valuations over intervals [c, c + 1], to an additive bidder. This is done by explicitly defining optimal dual solutions to a relaxed version of the problem, where the convexity requirement for the bidder’s utility has bee...

متن کامل

Obtaining Uniformly Dense Graphs

Let G be a non-trivial, loop-less multi-graph and for each non-trivial sub-graph H of G, let g(H) = |E(H)| |V (H)|−ω(G) . G is said to be uniformly dense if and only if γ(G), the maximum among g(H) taken over all non-trivial subgraphs H of G is attained when H = G. This quantity γ(G) is called the fractional arboricity of G and was introduced by Catlin, Grossman, Hobbs and Lai [4]. γ(G)− g(G) m...

متن کامل

Uniformly cordial graphs

LetG be a graph with vertex set V (G) and edge setE(G). A labeling f : V (G) → {0, 1} induces an edge labeling f ∗ : E(G) → {0, 1}, defined by f ∗(xy) = |f (x) − f (y)| for each edge xy ∈ E(G). For i ∈ {0, 1}, let ni(f ) = |{v ∈ V (G) : f (v) = i}| and mi(f )=|{e ∈ E(G) : f ∗(e)= i}|. Let c(f )=|m0(f )−m1(f )|.A labeling f of a graphG is called friendly if |n0(f )−n1(f )| 1. A cordial labeling ...

متن کامل

On uniformly balanced graphs

Let G = (V, E) be a simple graph. A vertex labeling f : V → {0, 1} induces a partial edge labeling f ∗ : E → {0, 1} defined by f ∗(uv) = f(u) 84 KWONG, LEE, LO, SU AND WANG if and only if f(u) = f(v). For i = 0, 1, let vf(i) = |{v ∈ V : f(v) = i}|, and ef (i) = |{e ∈ E : f ∗(e) = i}|. A graph G is uniformly balanced if |ef (0)−ef (1)| ≤ 1 for any vertex labeling f that satisfies |vf(0)−vf (1)| ...

متن کامل

Circadian clocks optimally adapt to sunlight for reliable synchronization

Circadian oscillation provides selection advantages through synchronization to the daylight cycle. However, a reliable clock must be designed through two conflicting properties: entrainability to synchronize internal time with periodic stimuli such as sunlight, and regularity to oscillate with a precise period. These two aspects do not easily coexist, because better entrainability favours highe...

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

ژورنال

عنوان ژورنال: Networks

سال: 2021

ISSN: ['0028-3045', '1097-0037']

DOI: https://doi.org/10.1002/net.22085