Aseem Dalal

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Recently Dalal and Govil [5] proved that, for any set of positive numbers {Ak}k=1 such that ∑n k=1 Ak = 1, a complex polynomial P (z) = ∑n k=0 dkz k (dk = 0, 0 ≤ k ≤ n) has all its zeros in the annulus A = {z : r1 ≤ |z| ≤ r2}, where r1 = min 1≤k≤n { Ak ∣∣∣d0 dk ∣∣∣ } 1 k and r2 = max 1≤k≤n { 1 Ak ∣∣∣dn−k dn ∣∣∣ } 1 k . This paper presents the best possible(More)
Social Networks play a very important role as a medium to propagate information among people. Marketers use this to campaign for their products and influence customers. However, it is not practically possible for a marketer to reach out to each and every individual prospective/existing customer due to the sheer size of the networks (in the orders of(More)
This paper makes progress towards settling the long-standing conjecture that the total chromatic number χ ′′ of the complete p-partite graph K = K(r1, . . . , rp) is ∆(K) + 1 if and only if K ≠ Kr,r and if K has an even number of vertices thenΣv∈V (K)(∆(K)−dK (v)) is at least the number of parts of odd size. Graphs of even order that are fairly close to(More)
A set of vertices in a graph is perfect dominating if every vertex outside the set is adjacent to exactly one vertex in the set, and is neighborhood connected if the subgraph induced by its open neighborhood is connected. In any graph the full set of vertices is perfect dominating, and in every connected graph the full set of vertices is neighborhood(More)
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