The Transmission Lemma from Rajasingh et al. (2016) is extended to the General Transmission Lemma. It gives a formula for the transmission of a vertex u as a function of a collection of edge cuts and a u-routing that uniformly intersects the edge cuts. The applicability of the General Transmission Lemma is demonstrated by computing the Wiener complexity of triangular grid networks. © 2018 Elsevier Inc.

Indra Rajasingh

Mathematics

School of Advanced Sciences

Chennai Campus

Manuel George

Department of Design and Automation

School of Mechanical Engineering

Vellore Campus

KlavÅ¾ar S

Azubha Jemilet D

Parthiban N.

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Applied Mathematics and Computation

Wiener index of a graph $G$ is defined as $W(G) = frac 12 sum {u,v in V(G)}

The Computer Journal

Transmission in Butterfly Networks

Matching is one of the most extensively studied areas in Computer Science and is interesting from the combinatorial point of view as well. A matching in a graph G=(V,E) is a subset M of edges, no two of which have a vertex in common. A matching M is said to be perfect if every vertex in G is an endpoint of one of the edges in M. The excessive index of a graph G is the minimum number of perfect matchings to cover the edge set of G. The study of excessive index has a number of applications particularly in scheduling theory. In this paper we determine the excessive index for certain classes of graphs including augmented butterfly network and honeycomb network. We also prove that the excessive index does not exist for butterfly and Benes networks. © 2013 Elsevier B.V.

Fulltext

Theoretical Computer Science

On excessive index of certain networks

On graphs whose Wiener complexity equals their order and on Wiener index of asymmetric graphs

Journal	Data powered by TypesetApplied Mathematics and Computation
Publisher	Data powered by TypesetElsevier BV
ISSN	0096-3003
Open Access	0