ABSTRACT In this paper the concept of upper edge geodetic domination number (UEGD number) and upper connected edge geodetic domination number (UCEGD number) of a graph is studied. An edge geodetic domination set (EGD set) S in a connected graph is minimal EGD set if no proper subset of S is an edge geodetic domination set. The maximum cardinality of all the minimal edge geodetic domination set is called UEGD number. An EGD set S in a connected graph is minimal CEGD set if no proper subset of S is a CEGD set. The maximum cardinality of all the minimal connected edge geodetic domination set is called UCEGD number. Here the UEGD number and UCEGD number of certain graphs are identified. Also for two positive integers p and q there exist some connected graph with EGD number p and UEGD number q. Similarly for two positive integers p and q there exist some connected graph with CEGD number p and UCEGD number q.
Keywords
Geodetic domination number, edge geodetic domination number, upper edge geodetic domination number, upper connected edge geodetic domination number.
AMS subject Classification: 05C12, 05C05
1 INTRODUCTION
By a graph G = (V, E) we consider a finite undirected graph without loops or multiple edges. The order and size of a graph are denoted by p and q respectively. For the basic graph theoretic notations and terminology we refer to Buckley and Harary [4].For vertices u and v in a connected graph G, the distance d(u, v) is the length of a shortest uv path in G. A
9) You are given the Class B network address: 172.25.0.0. From this network, if you needed to create 14 subnets, how many bits would need to be borrowed at a minimum and how many hosts could you have per subnet?
Use the network diagram below and the additional information provided to answer the corresponding questions. [15 points]
In this step, we take as input the graph $\overline{G} = (V, \overline{E})$ from the previous step and return graph $\widetilde{G}$ which has both both direct and CC links. The Figure \ref{top_cc} shows the output of step 2. In this graph, direct links $\overline{v_i v_j} \in E$ are shown in black and the CC links $\widetilde{v_i v_j} \in \overline{E}$ are shown in gray. Note that, the CC links are unidirectional, that is, the existence of $\widetilde{v_i v_j} \in \overline{E}$ does not imply $\widetilde{v_j v_i} \in
Exercise 2.3.4: It would take 1 hop to go from A to D, and from D to A. One additional link would connect E to the network, which would have no effect on sending messages.
Having obtained the edge information, the distances from nodes $n_2$ to $n_1$, $n_5$, and $n_6$ are computed.
In simulated network the source node designated as1 initiates the routing procedure by sending RREQ or Route Request message to its surrounding nodes. The RREQ message sent by the source node is denoted in the color green. The other RREQ messages are shown in cyan, yellow, black etc. The source node 1 is sending the RREQ message to its neighbour nodes 5, 6, 9, 11 and 13 and the links are formed shown by the green line. Every time node 5,6,9,11,13 is sending the RREQ message to its neighbour and the links are formed.
16. Consider the i-node shown in Fig. 4-13. If it contains 10 direct addresses and these
Step 1: Construct a network diagram for the project. (NOTE: EF for activity H should be 19)
Using the provided network diagram, write a program that finds the shortest path routing using the Bellman-Ford algorithm. Your program should represent the fact that your node is U. Show how the iterative process generates the routing table for your node. One of the keys to your program will be in determining when the iterative process is done.
From Chapter 6 in our textbook Experiencing Geometry by Henderson and Taimina, we formulated a summary of the properties of geodesics on the plane, spheres, and hyperbolic planes. I feel this is a good homework assignment to mention in this paper. For the first part of the problem we were to explain why for every geodesic on the plane, sphere, and hyperbolic plane there is a reflection of the whole space through the geodesic. For the second part of the problem I showed that every geodesic on the plane, sphere, and hyperbolic plane can be extended indefinitely (in the sense that the bug can walk straight ahead indefinitely along any geodesic). The third part asked to show that for every pair of distinct points on the plane, sphere, and hyperbolic plane there is a (not necessarily unique) geodesic containing them. In the fourth part of the problem I
The nodes on the bottom row represent sub-organizations, while the top two rows are individuals. (Organizational Hierarchy, page 1 para. 3) Old organizational models still exist in the real world where total control is a complete requirement. These old organizational models mainly used in government and military and sometimes transplanted to the non-military public companies and would work to a certain extent, but they have great limiting effect on promoting and evolving people.
2) Which of the following models determines the path through the network that connects all the points?
F. F. Bruce, "Galatian Problems. 2. North or South Galatians?" Bulletin of the John Rylands Library, no.
By simply inspecting the topological maps, it is not easy to know if one subway is better organized than the other (e.g., subway efficiency). One way to simplify this problem is to use metrics that quantify or analyze the subway network using graph theory [94, 101]. Hence the name of graph theoretical analysis.
The game Hex was invented by the Danish mathematician Piet Hein in the 1940s. This game has been of great interest to mathematicians around the world since its introduction, including Martin Gardner who explores it in chapter eight of his first Scientific American Book of Mathematical Puzzles and Games (1959). The game is normally played on a board of 11x11 hexagons with two edges labelled black and the other two labelled white. It is a two-person game in which both players (using black and white counters) attempt to create a chain connecting both of their respective sides of the board. This chapter will stray away from the basics of Hex and instead explore a more specific aspect of the game: ladders. Topics to be discussed include general