An edge dominating set of a graph is said to be an odd (even) sum degree edge dominating set (osded (esded) - set) of G if the sum of the degree of all edges in X is an odd (even) number. The odd (even) sum degree edge domination number is the minimum cardinality taken over all odd (even) sum degree edge dominating sets of G and is defined as zero if no such odd (even) sum degree edge dominating set exists in G. In this paper, the odd (even) sum degree domination concept is extended on the co-dominating set E-T of a graph G, where T is an edge dominating set of G. The corresponding parameters co-odd (even) sum degree edge dominating set, co-odd (even) sum degree edge domination number and co-odd (even) sum degree edge domination value is defined. Further, the exact values of the above said parameters are found for some standard classes of graphs. The bounds of the co-odd (even) sum degree edge domination number are obtained in terms of basic graph terminologies. The co-odd (even) sum degree edge dominating sets are characterized. The relationships with other edge domination parameters are also studied.
The exchanges in various fields,like economics, science, culture, etc., have been enhanced unceasingly among different countries around the world in the twenty-first century, thus, the university graduate who masters one foreign language does not meet the need of the labor market in most countries.So, many universities began to develop new programs to cultivate students who can use more foreign languages to serve the intercultural communication. At the same time, there is more scientific research emerged which is related to the relationship between the second and third languages. This humble research seeks to explain the relevant concepts and analyze the real data collected from Shanghai International Studies University in China, to expl
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The Central Bank is the backbone of the banking system as a whole, and in order to maintain the banking system, one of the most important functions that the Central Bank performs is the function of supervising and controlling banks, with several tools and methods, and one of the most important of these tools is its creation of the function of a compliance observer, which obligated commercial banks to appoint a person in A bank that performs this function according to certain conditions and granting it some powers that would build a sound and compliant banking system. The function of the compliance observer is to follow up on the bank’s compliance with the instructions and decisions issued by
... Show MoreZinc Oxide thin film of 2 μm thickness has been grown on glass substrate by pulsed laser deposition technique at substrate temperature of 500 oC under the vacuum pressure of 8×10-2 mbar. The optical properties concerning the absorption, and transmission spectra were studied for the prepared thin film. From the transmission spectra, the optical gap and linear refractive index of the ZnO thin film was determined. The structure of the ZnO thin film was tested with X-Ray diffraction and it was formed to be a polycrystalline with many peaks.
The fauna of bees (Hymenoptera, Apoidea) from different regions of Iraq is surveyed in this study; there were 16 species, 13 genera that belong to four families which are collected in this investigation.
Also, all the species that are recorded for Iraq in previous investigations are revised; totally there are 110 species, 32 genera belonging to five families: Apidae, Andernidae, Colletidae, Halictidae and Megachilidae were listed.
Gamma - irradiation effect on polymethylmethacrylate (PMMA) samples has been studied using Positron Annihilation Lifetime (PAL) method. The orthopositronium (o-Ps) lifetime τ3, hence the o-ps parameters, the volume hole size (Vh) and the free volume fraction (Ꞙh) in the irradiated samples were measured as a function of gamma-irradiation dose up to 28.05 kGy. It has been shown that τ 3, Vh, and Ꞙh, are increasing in general with increasing gamma-dose, to reach a maximum percentage increment of 22.42% in τ3, 60% in Vh and 29.5% in Ꞙh, at. 2.55 kGy, whereas τ2 reaches maximum increment of 119. 7% at 7.65 kGy. The results s
... Show MoreChitosan (CH) / Poly (1-vinylpyrrolidone-co-vinyl acetate) (PVP-co-VAc) blend (1:1) and nanocomposites reinforced with CaCO3 nanoparticles were prepared by solution casting method. FTIR analysis, tensile strength, Elongation, Young modulus, Thermal conductivity, water absorption and Antibacterial properties were studied for blend and nanocomposites. The tensile results show that the tensile strength and Young’s modulus of the nanocomposites were enhanced compared with polymer blend [CH/(PVP-co-VAc)] film. The mechanical properties of the polymer blend were improved by the addition of CaCO3 with significant increases in Young’s modulus (from 1787 MPa to ~7238 MPa) and tensile strength (from 47.87 MPa to 79.75 MPa). Strong interfacial
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