On the domination polynomials of friendship graphs

Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G,x)= n?i=0 d(G,i)xi, where d(G,i) is the number of dominating sets of G of size i. Let n be any positive integer and Fn be the Friendship graph with 2n + 1 vertices and 3n edges, formed by the join of K1 with nK2. We study the domination polynomials of this family of graphs, and in particular examine the domination roots of the family, and find the limiting curve for the roots. We also show that for every n > 2, Fn is not D-unique, that is, there is another non-isomorphic graph with the same domination polynomial. Also we construct some families of graphs whose real domination roots are only -2 and 0. Finally, we conclude by discussing the domination polynomials of a related family of graphs, the n-book graphs Bn, formed by joining n copies of the cycle graph C4 with a common edge.

Signless Laplacian spectral characterization of graphs with isolated vertices

A graph is said to be DQS if there is no other non-isomorphic graph with the same signless Laplacian spectrum. For a DQS graph G, we show that G ? rK1 is DQS under certain conditions. Applying these results, some DQS graphs with isolated vertices are obtained.

Proposed Isomorphic Graph Model for Risk Assessment on a Unix Operating System

Control and risk are the two parts of the coin. Risk assessment is the process of identifying uncertainties, vulnerabilities and threats to the operating system resources in order to achieve business objectives. Risk evaluation involved deciding what counter measures to take in reducing uncertainty to the lowest level of risk. Control is probably the most important aspect of communications security and becoming increasingly important as basic building block for system security. Advanced Encryption Standard (AES) is a primary method of protecting system resources. AES is inversely proportional to the Risk (C=K/R) & mean while control is directly proportional to the quality of standard. AES Control will be optimize the risk as well as improve the IS standard. Control is directly proportional to risk mitigation & mitigation is directly proportional to standard. This paper contributes to the development of an optimization method that aims to determine the optimal cost to be invested into security method, model & mechanisms deciding on the measure component of operating system resources (i.e. Processor, Memory & Encryption). Furthermore, the method & mechanism optimize the cost, time & resources is supposed to optimize the system risks. The proposed model would be update the value of Processor, Memory & Encryption key dynamically as per business requirement and availability of technology & resources. Proposed model is going to be optimizing risk and maximizing the performance. In this study the researchers develop an isomorphic graph model for optimizing risk in the Unix operating system.

Proof of Four Color Map Theorem by Using PRN of Graph

This paper intends to study the relation between PRN and chromatic number of planar graphs. In this regard we investigate that isomorphic or 1 isomorphic graph may or may not have equal PRN and few other related results. Precisely, we give simple proof of Four Color Map Theorem.

Proposed Isomorphic Graph Model for Risk Assessment on a Unix Operating System

Control and risk are the two parts of the coin. Risk assessment is the process of identifying uncertainties, vulnerabilities and threats to the operating system resources in order to achieve business objectives. Risk evaluation involved deciding what counter measures to take in reducing uncertainty to the lowest level of risk. Control is probably the most important aspect of communications security and becoming increasingly important as basic building block for system security. Advanced Encryption Standard (AES) is a primary method of protecting system resources. AES is inversely proportional to the Risk (C=K/R) & mean while control is directly proportional to the quality of standard. AES Control will be optimize the risk as well as improve the IS standard. Control is directly proportional to risk mitigation & mitigation is directly proportional to standard. This paper contributes to the development of an optimization method that aims to determine the optimal cost to be invested into security method, model & mechanisms deciding on the measure component of operating system resources (i.e. Processor, Memory & Encryption). Furthermore, the method & mechanism optimize the cost, time & resources is supposed to optimize the system risks. The proposed model would be update the value of Processor, Memory & Encryption key dynamically as per business requirement and availability of technology & resources. Proposed model is going to be optimizing risk and maximizing the performance. In this study the researchers develop an isomorphic graph model for optimizing risk in the Unix operating system.