Eyes with refractory macular edema showed improvement of visual acuity and reduction of CSFT at three months when treated with combined IVTA and IVB.
In this paper, a new concept k -size edge resolving set for a connected graph G in the context of resolvability of graphs is defined. Some properties and realizable results on k -size edge resolvability of graphs are studied. The existence of this new parameter in different graphs is investigated, and the k -size edge metric dimension of path, cycle, and complete bipartite graph is computed. It is shown that these families have unbounded k -size edge metric dimension. Furthermore, the k-size edge metric dimension of the graphs Pm □ Pn, Pm □ Cn for m, n ≥ 3 and the generalized Petersen graph is determined. It is shown that these families of graphs have constant k -size edge metric dimension.
For a connected graph G = V G , E G , let v ∈ V G be a vertex and e = uw ∈ E G be an edge. The distance between the vertex v and the edge e is given by d G e , v = min d G u , v , d G w , v . A vertex w ∈ V G distinguishes two edges e 1 , e 2 ∈ E G if d G w , e 1 ≠ d G w , e 2 . A well-known graph invariant related to resolvability of graph edges, namely, the edge resolving set, is studied for a family of 3 -regular graphs. A set S of vertices in a connected graph G is an edge metric generator for G if every two edges of G are distinguished by some vertex of S . The smallest cardinality of an edge metric generator for G is called the edge metric dimension and is denoted by β e G . As a main result, we investigate the minimum number of vertices which works as the edge metric generator of double generalized Petersen graphs, DGP n , 1 . We have proved that β e DGP n , 1 = 4 when n ≡ 0,1,3 mod 4 and β e DGP n , 1 = 3 when n ≡ 2 mod 4 .
The entire security landscape of the world was altered due to the 9/11 terrorist attacks on America's World Trade Centre. After this incident, the US accused Al-Qaeda headship of the attacks. Henceforth, President Bush demanded the Afghan Taliban hand over Osama Bin Laden to the US. However, when the Taliban did not respond positively, the US attacked Afghanistan. The US also pushed Pakistan to take a U-turn on its Afghan policy; hence, President Musharraf decided to offer logistics and other relevant backing to the American force sin their operation in Afghanistan. After the defeat of the Afghan Taliban in 2002, many militants from Afghanistan came to Pakistan's tribal areas through a porous border. As Pakistan supported the US War on Terrorism (WoT), a militant insurgency was started in the tribal areas of Pakistan. This research examines the counter-terrorism strategies of the Pakistan army that it implemented from 2009 to 2016. The study explains the military operations of the Pakistan army in former FATA against hardcore terrorist groups like Tehreek-i-Taliban Pakistan (TTP) and other small and affiliated radical organizations. It is analyzed that military operations namely Rah-e-Nijat and Zarb-e-Azb in former FATA with a focus on North and South Waziristan relatively remained successful.
The edge H -irregularity strength, e h s Γ , H , of a graph Γ is the smallest integer k , such that Γ has an H -irregular edge k -labeling. In this study, we compute the exact value of edge H -irregularity strength of hexagonal and octagonal grid graphs.
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