Jaem 2017, Vol 7, No 1Jaem 2017, Vol 7, No 1 koleksiyonunu içerir.https://hdl.handle.net/11729/24002022-08-12T22:06:39Z2022-08-12T22:06:39ZA note on line graphsSatyanarayana, BhavanariSrinivasulu, DevanaboinaSyam Prasad, Kunchamhttps://hdl.handle.net/11729/26212021-07-01T11:11:30Z2017-02-20T00:00:00ZA note on line graphs
Satyanarayana, Bhavanari; Srinivasulu, Devanaboina; Syam Prasad, Kuncham
The line graph and 1-quasitotal graph are well-known concepts in graph theory. In Satyanarayana, Srinivasulu, and Syam Prasad [13], it is proved that if a graph G consists of exactly m connected components Gi (1 ≤ i ≤ m) then L(G) = L(G1) = L(G2) ⊕ ... ⊕ L(Gm) where L(G) denotes the line graph of G, and ⊕ denotes the ring sum operation on graphs. In [13], the authors also introduced the concept 1- quasitotal graph and obtained that Q1(G) = G⊕L(G) where Q1(G) denotes 1-quasitotal graph of a given graph G. In this note, we consider zero divisor graph of a finite associate ring R and we will prove that the line graph of Kn−1 contains the complete graph on n vertices where n is the number of elements in the ring R.
2017-02-20T00:00:00ZNumerical solution of a 2D- diffusion reaction problem modelling the density of di-vacancies and vacancies in a metalPamuk, Serdalhttps://hdl.handle.net/11729/26202021-07-01T11:12:22Z2017-01-03T00:00:00ZNumerical solution of a 2D- diffusion reaction problem modelling the density of di-vacancies and vacancies in a metal
Pamuk, Serdal
A decomposition solution of a diffusion reaction problem, which models the density of di-vacancies and vacancies in a metal is presented. The results are compared with the numerical solutions. Zero - diffusion solutions are obtained numerically and some figures are illustrated.
2017-01-03T00:00:00ZPartitioning a graph into monopoly setsNaji, Ahmed MohammedNandappa D., Sonerhttps://hdl.handle.net/11729/26192021-07-01T11:17:11Z2017-01-01T00:00:00ZPartitioning a graph into monopoly sets
Naji, Ahmed Mohammed; Nandappa D., Soner
In a graph G = (V, E), a set M ⊆ V (G) is said to be a monopoly set of G if every vertex v ∈ V − M has, at least, d(v)/2 neighbors in M. The monopoly size of G, denoted by mo(G), is the minimum cardinality of a monopoly set. In this paper, we study the problem of partitioning V (G) into monopoly sets. An M-partition of a graph G is the partition of V (G) into k disjoint monopoly sets. The monatic number of G, denoted by µ(G), is the maximum number of sets in M-partition of G. It is shown that 2 ≤ µ(G) ≤ 3 for every graph G without isolated vertices. The properties of each monopoly partite set of G are presented. Moreover, the properties of all graphs G having µ(G) = 3, are presented. It is shown that every graph G having µ(G) = 3 is Eulerian and have χ(G) ≤ 3. Finally, it is shown that for every integer k /∈ {1, 2, 4}, there exists a graph G of order n = k having µ(G) = 3.
2017-01-01T00:00:00ZAdaptive methods for solving operator equations by using frames of subspacesJamali, HassanShokri, Khadijehhttps://hdl.handle.net/11729/26182021-07-01T11:18:25Z2017-01-01T00:00:00ZAdaptive methods for solving operator equations by using frames of subspaces
Jamali, Hassan; Shokri, Khadijeh
In this paper, using a frame of subspaces we transform an operator equation to an equivalent `2-problem. Then, we propose an adaptive algorithm to solve the problem and investigate the optimality and complexity properties of the algorithm.
2017-01-01T00:00:00Z