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Graphs from Total Graphs,In this chapter, we study certain graphs obtained from total graphs of commutative rings. More specifically, we concentrate on the total graph without the zero element, the complement of the total graph, and its generalizations.

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https://doi.org/10.1007/978-81-322-1865-4ph on a surface so that no two edges cross, an intuitive geometric problem that can be enriched by specifying symmetries or combinatorial side-conditions. Graphs on surfaces form a natural link between discrete and continuous mathematics.

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https://doi.org/10.1007/978-981-19-2370-8graph. In variation to this, a graph using the addition of the ring is constructed and is called the total graph of commutative rings. The next several chapters of this book are devoted to this notion of total graph.

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Introduction,, we state some definitions and notation used throughout to keep this book as self-contained as possible. This chapter includes some basic definitions and results which are needed for the subsequent chapters.

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Total Graphs of Commutative Rings,graph. In variation to this, a graph using the addition of the ring is constructed and is called the total graph of commutative rings. The next several chapters of this book are devoted to this notion of total graph.