Soil erosion and sediment yield from watershed are among key limitations to achieve sustainable land use and to maintain the water quality. Development of the sediment graph (SG) is essentially required for accurate estimation of sediment yield from the watershed. However, development of SGs for watersheds is a tedious and time consuming task. Development of the sediment graph models based on easily accessible physical characteristics of a watershed and precipitation data is therefore a viable and convenient tool for designing the efficient soil and water conservation measures. In this regard, driving synthetic SGs using instantaneous Unit sediment graph (IUSG) is an applied approach in watersheds where detailed discharge and sediment data are not available. However, the performance of this approach in watershed scale with different governing conditions has rarely been evaluated. The present study formulated IUSG for Kojour watershed comprising an area of some 500 Km2. The Watershed located at east of Nowshahr City in Mazandaran Province, northern Iran. The suspended sediment samples were taken from Kojour River during eight storm events in 2008 and corresponding SGs were then developed. The results showed that the IUSG model is unable to predict observed SGs components of peak, time to peak, total sediment yield, and the base time having respective estimation errors of 764, 111,750 and 101%.

In this paper, we have characterized the commutative rings with Unity for which line signed graph of a signed Unit graph is balanced and consistent. To do this, we first establish some sufficient conditions for balance and consistency of line signed graph of signed Unit graphs.

Instantaneous Unit sediment graph (IUSG) is one of the methods for predicting sediment graph of the flood events and its application needs to estimation of storage coefficient (Ks), dimensionless shape factor (ns), time to peak (tp) and instantaneous sediment supply. Investigation of relationships among the mentioned parameters and rainfall and water discharge characteristics could facilitates use of IUSG in ungaged drainage basins. In this research concurrent flow and sediment discharge of five flood events in Poledouab hydrometric station monitored hourly .IUSG parameters calculated using observed sediment graphs and rainfall hyetographs and their relationship investigated with excess rainfall and peak water discharge of flood events. The results show that correlation coefficient (r2) of power regression equation between Ks and rainfall excess is greater than peak flow (0.79 and 0.42).dimensionless shape factor of ns shows statistically weak relationship with rainfall excess and peak flow but its ratio to time to peak of sediment graph (ns/tp) resulted in statistically meaningful relationship with the rainfall excess and peak flow (respectively 0.85 and 0.67 of r2).application of the obtained equations in this research for predicting sediment graph of some flood hydrographs and comparing the results with the sediment rating curve methods show that rising limb of the sediment graph could be predicted more accurately than falling limb of sediment graph.

The Unit disk graph is used to model a wireless sensor network when all sensors have the same communication radius. Hence, the following two optimization problems have been investigated by the researchers: maximal independent set in the network and minimal network dominating set. Since these problems are Np-hard, several algorithms have been presented for their approximation. In this paper, we have presented a honeycomb graph and algorithmic matrix methods for approximating the maximal independent set in the network. Finally, we have confirmed the validity of the algorithm and its complexity and studied it with a numerical example.

The independence graph Ind(G) of a graph G is the graph with vertices as maximum independent sets of G and two vertices are adjacent, if and only if the corresponding maximum independent sets are disjoint. In this work, we find the independence graph of Cartesian product of d copies of complete graphs Kq, which is known as the Hamming graph H(d, q). Greenwell and Lovasz [7] found that the independence number of direct product of d copies of Kq as qd−1. We prove that the independence number of Hamming graph H(d, q), which is cartesian product of d copies of Kq, is also qd−1. As an application of our findings, we find answers for rook problem in higher dimensional square chess board.

In this paper, we find the star chromatic number of central graph of complete bipartite graph and corona graph of complete graph with path and cycle.

Let R be a commutative ring and M be an R-module. The M-intersection graph of ideals of R, denoted by GM(R) is a graph with the vertex set I(R) ∗, , and two distinct vertices I and J are adjacent if and only if IM ∩,JM ̸, = 0. In this paper, we study GR/J (R/I), where I and J are ideals of R and I ⊆,J. We characterize all ideals I and J for which GR/J (R/I) is planar, outerplanar or ring graph.

‎graph coloring is the assignment of one color to each vertex of a graph so that two adjacent vertices are not of the same color‎. ‎The graph coloring problem (GCP) is a matter of combinatorial optimization‎, ‎and the goal of GCP is determining the chromatic number $\chi(G)$‎. ‎Since GCP is an NP-hard problem‎, ‎then in this paper‎, ‎we propose a new approximated algorithm for finding the coloring number (it is an approximation of chromatic number) by using a graph adjacency matrix to colorize or separate a graph‎. ‎To prove the correctness of the proposed algorithm‎, ‎we implement it in MATLAB software‎, ‎and for analysis in terms of solution and execution time‎, ‎we compare our algorithm with some of the best existing algorithms that are already implemented in MATLAB software‎, ‎and we present the results in tables of various graphs‎. ‎Several available algorithms used the largest degree selection strategy‎, ‎while our proposed algorithm uses the graph adjacency matrix to select the vertex that has the smallest degree for coloring‎. ‎We provide some examples to compare the performance of our algorithm to other available methods‎. ‎We make use of the Dolan-Mor\'e performance profiles to assess the performance of the numerical algorithms‎, ‎and demonstrate the efficiency of our proposed approach in comparison with some existing methods‎.