Epstein-Barr virus (EBV), a member of the herpes virus family, is a causative agent for infectious mononucleosis in young adults. It has an asymptomatic and subclinical distribution in about 90% to 95% of the world population based on seropositivity. EBV is associated with various lymphomas, nasopharyngeal carcinoma, and in immunocompromised states can give rise to aggressive lymphoproliferative disorders. Symptomatic patients mostly present with mild hepatitis, rash, oral symptoms, lymphadenopathy, and generalized malaise. Recently with the COVID-19 (coronavirus disease-2019) pandemic, hepatitis has been found to be related to acute EBV and cytomegalovirus reactivation versus acute infection in the absence of other major causes. We describe a case of EBV coinfection in a patient with resolving mild COVID-19 infection.

The partition dimension is a variant of metric dimension in graphs. It has arising applications in the fields of network designing, robot navigation, pattern recognition and image processing. Let G (V (G) , E (G)) be a connected graph and Γ = {P1, P2, …, Pm} be an ordered m-partition of V (G). The partition representation of vertex v with respect to Γ is an m-vector r (v|Γ) = (d (v, P1) , d (v, P2) , …, d (v, Pm)), where d (v, P) = min {d (v, x) |x ∈ P} is the distance between v and P. If the m-vectors r (v|Γ) differ in at least 2 positions for all v ∈ V (G), then the m-partition is called a 2-partition generator of G. A 2-partition generator of G with minimum cardinality is called a 2-partition basis of G and its cardinality is known as the 2-partition dimension of G. Circulant graphs outperform other network topologies due to their low message delay, high connectivity and survivability, therefore are widely used in telecommunication networks, computer networks, parallel processing systems and social networks. In this paper, we computed partition dimension of circulant graphs Cn (1, 2) for n ≡ 2 (mod 4), n ≥ 18 and hence corrected the result given by Salman et al. [Acta Math. Sin. Engl. Ser. 2012, 28, 1851-1864]. We further computed the 2-partition dimension of Cn (1, 2) for n ≥ 6.

In any interconnection network, fault tolerance is the most desirable property to achieve reliability. Toeplitz networks are used as interconnection networks due their smaller diameter, symmetry, simpler routing, high connectivity, and reliability. The partition dimension of a network is presented as an extension of metric dimension of networks. Its applications can be seen in several areas including robot navigation, network designing, image processing, and chemistry. In this article, the fault tolerant partition dimension, pd 2 T n 1 , t , of Toeplitz networks, is shown to be bounded below by 4 for t ≥ 2 , n ≥ 4 , whereas it is bounded above by 5 for t = 3 , n ≥ 14 . Further, it is shown that the exact value of pd 2 T n 1 , t equals 4 for t = 2 , n ≥ 4 ; t = 3 , n ∈ 5,6 , … , 13 ; and t ≥ 4 , n ∈ t + 2 , t + 3 , t + 4 .

The symmetry of an interconnection network plays a key role in defining the functioning of a system involving multiprocessors where thousands of processor-memory pairs known as processing nodes are connected. Addressing the processing nodes helps to create efficient routing and broadcasting algorithms for the multiprocessor interconnection networks. Oxide interconnection networks are extracted from the silicate networks having applications in multiprocessor systems due to their symmetry, smaller diameter, connectivity and simplicity of structure, and a constant number of links per node with the increasing size of the network can avoid overloading of nodes. The fault tolerant partition basis assigns unique addresses to each processing node in terms of distances (hops) from the other subnets in the network which work in the presence of faults. In this manuscript, the partition and fault tolerant partition resolvability of oxide interconnection networks have been studied which include single oxide chain networks (SOXCN), rhombus oxide networks (RHOXN) and regular triangulene oxide networks (RTOXN). Further, an application of fault tolerant partition basis in case of region-based routing in the networks is included.