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2016•International Journal of Mathematical ArchiveRequires access

• RELATION BETWEEN TOTAL DOMINATION NUMBER, ENERGY OF A GRAPH AND RANK

Manjula C. Gudgeri, Shailaja S. Shirkol, Pallavi I. Kalmath Varsha

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Abstract

D omination theory and energy of a graph are the fastest growing areas within graph theory. The energy of a graph is defined as the sum of the absolute values of all eigen values of its adjacency matrix of a graph. In this paper we present some sharp lower bounds which relate total domination number of a graph G, energy of G and rank of the incident matrix of some class of graphs.

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What this paper is about

D omination theory and energy of a graph are the fastest growing areas within graph theory. The energy of a graph is defined as the sum of the absolute values of all eigen values of its adjacency matrix of a graph. In this paper we present some sharp lower bounds which relate total domination number of a graph G, energy of G and rank of the incident matrix of some class of graphs.

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Available abstract

D omination theory and energy of a graph are the fastest growing areas within graph theory. The energy of a graph is defined as the sum of the absolute values of all eigen values of its adjacency matrix of a graph. In this paper we present some sharp lower bounds which relate total domination number of a graph G, energy of G and rank of the incident matrix of some class of graphs.

Key concepts: Graph energy, Adjacency matrix, Mathematics, Combinatorics, Line graph, Butterfly graph, Regular graph, Voltage graph

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