A Note on the Inverse Connected <i>p</i>-Median Problem on Block Graphs

نویسندگان

چکیده

Recently, the inverse connected p-median problem on block graphs G(V,E,w) under various cost functions, say rectilinear norm, Chebyshev and bottleneck Hamming distance. Their contributions include finding a necessary sufficient condition for graphs, developing algorithms showing that these problems can be solved in O(n log n) time, where n is number of vertices underlying graph. Using similar technique, we show some results are incorrect by counter-example. Then redefine notations, reprove Theorem 1 redescribe 2, 3 4.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود 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

Locating Median Paths on Connected Outerplanar Graphs

During the last two decades, there has been a growing interest in locating extensive facilities, such as paths, on networks. In this paper we study the median path problem without restrictions on its length on the class of connected outerplanar graphs with equal weights assigned to the edges and nonnegative weights associated to the vertices. We provide a O(kn) time algorithm, where n is the nu...

متن کامل

A note on minimally 3-connected graphs

If G is a minimally 3-connected graph and C is a double cover of the set of edges of G by irreducible walks, then |E (G)| ≥ 2 |C| − 2.

متن کامل

The median problem on k-partite graphs

In a connected graph G, the status of a vertex is the sum of the distances of that vertex to each of the other vertices in G. The subgraph induced by the vertices of minimum (maximum) status in G is called the median (anti-median) of G. The median problem of graphs is closely related to the optimization problems involving the placement of network servers, the core of the entire networks. Bipart...

متن کامل

A note on vague graphs

In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.

متن کامل

Note on minimally k-connected graphs

A k-tree is either a complete graph on (k+1) vertices or given a k-tree G′ with n vertices, a k-tree G with (n+1) vertices can be constructed by introducing a new vertex v and picking a k-clique Q in G′ and then joining each vertex u in Q. A graph G is kedge-connected if the graph remains connected even after deleting fewer edges than k from the graph. A k-edge-connected graph G is said to be m...

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: Advances in Pure Mathematics

سال: 2023

ISSN: ['2160-0368', '2160-0384']

DOI: https://doi.org/10.4236/apm.2023.134011