The Footprint of Things: A hybrid approach towards the collection, storage and distribution of life cycle inventory data

Life cycle assessment is a well-established methodology for assessing the environmental impacts of products and services. Unfortunately, an essential part of this life cycle assessment method, collecting inventory data, is extremely time consuming. The quality of manually conducted LCA studies is often limited by uncertainty in the inventory data or narrow scope. Past attempts to overcome these challenges through automation of data collection utilizing the Internet of Things have relied on fully centralized architectures. The drawback of a central repository is the complex coordination between all involved actors in supply chains of products and services. This paper proposes an alternative hybrid approach combining a primary distributed system supplemented with a central repository reducing the need for coordination. This hybrid approach is named "the Footprint of Things". We present a system design that embeds the automatic reporting of life cycle inventory data, such as energy and material flows, into all product components involved in a service delivery. The major strength of our novel system design, among others, is its capacity for real-time and more precise impact calculation of ICT services

L(d,2,1)-Labeling of Star and Sun Graphs

For positive integer d, L(d,2,1)-labeling of a graph G is a function f from V(G) to the positive integers, f: V(G) {1, 2,…} such that |f(u) – f(v)| ≥ d if the distance between any 2 vertices u and v is 1 (D(u,v) =1), |f(u) – f(v)| ≥ 2 if D(u,v) = 2, and |f(u) – f(v)| ≥ 1 if D(u,v) = 3. The L(d,2,1)-labeling number kd(G) of a graph G is the smallest positive integer kd such that G has an L(d,2,1)-labeling with kd as the maximum label. This paper presents a general kd-value of stars K1,n and kd-value of sun graphs Sn for d = 3. Keywords: L(d,2,1)-Labeling, distance, L(d,2,1)-Labeling number, sun graphs, stars