Locating and Identifying Codes in Circulant Graphs

Identifying and locating-dominating codes have been studied widely in circulant graphs. Recently, Ville Junnila et al. (Optimal bounds on codes for location in circulant graphs, Cryptography and Communications; 2019) studied identifying and locating-dominating codes in circulants C n 1 , d , C n 1 , d − 1 , d , and C n 1 , d − 1 , d , d + 1 . In this paper, identifying, locating, and self-identifying codes in the circulant graphs C n k , d , C n k , d − k , d , and C n k , d − k , d , d + k are studied, and this extends Junnila et al.’s results to general cases.

PP17 Development and application of a clinical risk stratification tool using routine data from electronic patient clinical records

BackgroundFollowing the introduction of electronic patient clinical records, ambulance service managers wished to combine clinical and operational data to devise a method of risk stratifying 999 calls by the MPDS disposition code assigned at call triage. Initial aims were to establish the risk threshold if an ambulance was no longer routinely dispatched.MethodsData selected were representative of high or low clinical risk, and reliably recorded. The following ‘risk factors’ were chosen:Call outcomeEmergency conditionsClinical interventionsMedications administeredWith expert local opinion, a scoring algorithm was created using weighted factor scores to create an aggregate risk score for each MPDS code. It was also designed to distribute codes along a ‘risk range’, allowing for thresholds setting suitable to the specific purpose of individual projects. These factors and their scores were captured alongside contextual information and to date contains over 1.4 million records over 3 years.In collaboration with academic colleagues, we also developed an AI model to refine the algorithm used to reflect acuity. With one year of data the tool did not demonstrate the sensitivity or specificity to reliably contribute to prediction, however this exercise may be repeated now there is a greater volume of data.Applications: This Tool has been successfully used for a variety of purposes:Developing the Enhanced Hear and Treat policyAssessing risk of code downgrades in the pandemic responseIdentifying codes suitable for automatic specialist clinician allocationsSupplementing analysis of harm caused by long response delaysIdentifying codes for protection within End of Shift protocolsProviding intelligence to aid national decisions on code categorisationNext steps: The Tool continues to assist in decision-making locally. Future ambitions include:Validation of the scoring algorithmsProcess automation to ensure more timely data is availableCollaboration to improve the variety and volume of data

Optimal Identifying Codes in Oriented Paths and Circuits

Identifying codes in graphs are related to the classical notion of dominating sets [1]. Since there first introduction in 1998 [2], they have been widely studied and extended to several application, such as: detection of faulty processor in multiprocessor systems, locating danger or threats in sensor networks. Let G=(V,E) an unoriented connected graph. The minimum identifying code in graphs is the smallest subset of vertices C, such that every vertex in V have a unique set of neighbors in C. In our work, we focus on finding minimum cardinality of an identifying code in oriented paths and circuits

Covering codes of a graph associated to a finite vector space

UDC 512.5 In this paper, we investigate the problem of covering the vertices of a graph associated to a finite vector space as introduced by Das [Commun. Algebra, <strong>44</strong>, 3918 – 3926 (2016)], such that we can uniquely identify any vertex by examining the vertices that cover it. We use locating-dominating sets and identifying codes, which are closely related concepts for this purpose. We find the location-domination number and the identifying number of the graph and study the exchange property for locating-dominating sets and identifying codes.

Minimum identifying codes in some graphs differing by matchings

For a vertex [Formula: see text] of a graph [Formula: see text], let [Formula: see text] be the set of [Formula: see text] with all of its neighbors in [Formula: see text]. A set [Formula: see text] of vertices is an identifying code of [Formula: see text] if the sets [Formula: see text] are nonempty and distinct for all vertices [Formula: see text] of [Formula: see text]. If [Formula: see text] admits an identifying code, then [Formula: see text] is called identifiable and the minimum cardinality of an identifying code of [Formula: see text] is denoted by [Formula: see text]. Let [Formula: see text] be two positive integers. In this paper, [Formula: see text] and [Formula: see text] are computed, where [Formula: see text] and [Formula: see text] represent the complement of a path and the complement of a cycle of order [Formula: see text], respectively. Among other results, [Formula: see text] is given, where [Formula: see text] is obtained from [Formula: see text] after deleting a maximum matching.