Browsing by Author "Durgun, DD"
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Item Weak and strong domination on some graphsDurgun, DD; Kurt, BLLet G = (V(G), E(G)) be a graph and uv epsilon E. A subset D subset of V of vertices is a dominating set if every vertex in V - D is adjacent to at least one vertex of D. The domination number is the minimum cardinality of a dominating set. Let u and v be elements of V. Then, u strongly dominates u and v weakly dominates u if (i)uv epsilon E and (ii)deg(u) >= deg(v). A set D subset of V is a strong (weak) dominating set (sd-set)(wd-set) of G if every vertex in V - D is strongly dominated by at least one vertex in D. The strong (weak) domination number gamma(s)(gamma(w)) of G is the minimum cardinality of a sd-set (wd-set). In this paper, the strong and weak domination numbers of comet, double comet, double star and theta graphs are given. The theta graphs are important geometric graphs that have many applications, including wireless networking, motion planning, MST construction and real-time animation.Item Weak and strong domination in thorn graphsDurgun, DD; Lökçü, BLet G = (V, E) be a graph and u, v is an element of V. A dominating set D is a set of vertices such that each vertex of G is either in D or has at least one neighbor in D. The minimum cardinality of such a set is called the domination number of G, gamma(G). u strongly dominates v and v weakly dominates u if (i) uv is an element of E and (ii) deg u >= deg v. A set D subset of V is a strong-dominating set, shortly sd-set, (weak-dominating set, shortly wd-set) of G if every vertex in V - D is strongly (weakly) dominated by at least one vertex in D. The strong (weak) domination number gamma(s)(gamma(w)) of G is the minimum cardinality of an sd-set (wd-set). In this paper, we present weak and strong domination numbers of thorn graphs.Item AVERAGE COVERING NUMBER FOR SOME GRAPHSDurgun, DD; Bagatarhan, AThe interconnection networks are modeled by means of graphs to determine the reliability and vulnerability. There are lots of parameters that are used to determine vulnerability. The average covering number is one of them which is denoted by (beta) over bar (G) , where G is simple, connected and undirected graph of order n >= 2. In a graph G = (V (G), E(G)) a subset S-v subset of V (G) of vertices is called a cover set of G with respect to v or a local covering set of vertex v, if each edge of the graph is incident to at least one vertex of S-v. The local covering number with respect to v is the minimum cardinality of among the S-v sets and denoted by beta(v) The average covering number of a graph G is defined as (beta) over bar (G) = 1/vertical bar V(G)vertical bar Sigma(v is an element of V(G)) beta(v). In this paper, the average covering numbers of kth power of a cycle C-n(k) and P-n square p(m), P-n, square C-m, cartesian product of P-n, and P-m cartesian product of P-n, and C-m are given, respectively.Item PACKING CHROMATIC NUMBER OF TRANSFORMATION GRAPHSDurgun, DD; Dortok, HBOGraph coloring is an assignment of labels called colors to elements of a graph. The packing coloring was introduced by Goddard et al. [1] in 2008 which is a kind of coloring of a graph. This problem is NP-complete for general graphs. In this paper, we consider some transformation graphs and generalized their packing chromatic numbers.Item AN ANALYTICAL STUDY ON THE ENTROPY GENERATION IN FLOW OF A GENERALIZED NEWTONIAN FLUIDAksoy, Y; Gurkan, N; Aksoy, AB; Durgun, DD; Yurddas, AIn this study, an analytical investigation on pressure driven flow of Powell-Eyring fluid is conducted to understand the irreversibilities due to heat transfer and viscous heating. The flow between infinitely long parallel plates is considered as fully developed and laminar with constant properties and subjected to symmetrical heat fluxes from solid boundaries. The internal heating due to viscous friction accompanies external heat transfer, that is, viscous dissipation term is to be involved in the energy equation. As a cross-check, accuracy of analytical solutions is confirmed by a predictor-corrector numerical scheme with variable step size.