Aleksandar Jurisic

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In recent years, in urban areas of Novi Sad, unique ecological conditions, specific floristic and faunistic composition and poor habits of citizens in sense of public health, facilitate the development and maintenance of ticks. Regarding the importance of ticks as vectors of severe human and animal diseases, complex and detailed studies are conducted with(More)
Let ? be a distance-regular graph with diameter d. For vertices x and y of ? at distance i, 1 i d, we deene the sets (x) \ ?(y). Then we say ? has the CAB j property, if the partition CAB i (x; y) = fC i (x; y); A i (x; y); B i (x; y)g of the local graph of y is equitable for each pair of vertices x and y of ? at distance i j. We show that if ? has the CAB(More)
Antipodal covers of strongly regular graphs which are not necessarily distance-regular are studied. The structure of short cycles in an antipodal cover is considered. In most cases, this provides a tool to determine if a strongly regular graph has an antipodal cover. In these cases, covers cannot be distance-regular except when they cover a complete(More)
In this paper, triangle-free distance-regular graphs with diameter 3 and an eigenvalue θ with multiplicity equal to their valency are studied. Let Γ be such a graph. We first show that θ = −1 if and only if Γ is antipodal. Then we assume that the graph Γ is primitive. We show that it is formally self-dual (and hence Q-polynomial and 1-homogeneous), all its(More)
We classify triangle-and pentagon-free distance-regular graphs with diameter d ≥ 2, valency k, and an eigenvalue multiplicity k. In particular, we prove that such a graph is isomorphic to a cycle, a k-cube, a complete bipartite graph minus a matching, folded k-cube, k odd and k ≥ 7. This is a generalization of the results of Nomura [10] and Yamazaki [13],(More)
Let Γ be a triangle-free distance-regular graph with diameter d ≥ 3, valency k ≥ 3 and intersection number a 2 = 0. Assume Γ has an eigenvalue with multiplicity k. We show that Γ is 1-homogeneous in the sense of Nomura when d = 3 or when d ≥ 4 and a 4 = 0. In the latter case we prove that Γ is an antipodal cover of a strongly regular graph, which means that(More)