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2018•Journal of Emerging Technologies and Innovative ResearchRequires access

CHARACTERIZATION OF SOME SPECIAL CLASSES OF GRAPHS

Anu Mathew, Timmy Tomy Thalavayalil

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Abstract

Graph theory is an applied branch of mathematics which deals with problems with the help of graphs. One of the popular areas of research in graph theory is the study of the graphs that are obtained from given graphs. Concept of total graph comes under this category. Every graph has a total graph but all graphs are not total graphs of some graph. The total graph T(G) of G is the graph whose vertex set corresponds to the set of vertices and edges of G such that two vertices of T(G) are adjacent if and only if the corresponding elements of G are adjacent or incident. This paper gives formulas to find the regularity, the number of triangles and the number of edges of total graphs of certain standard graphs like path graph, complete graph cyclic graph.

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What this paper is about

Graph theory is an applied branch of mathematics which deals with problems with the help of graphs. One of the popular areas of research in graph theory is the study of the graphs that are obtained from given graphs. Concept of total graph comes under this category. Every graph has a total graph but all graphs are not total graphs of some graph. The total graph T(G) of G is the graph whose vertex set corresponds to the set of vertices and edges of G such that two vertices of T(G) are adjacent if and only if the corresponding elements of G are adjacent or incident. This paper gives formulas to find the regularity, the number of triangles and the number of edges of total graphs of certain standard graphs like path graph, complete graph cyclic graph.

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Available abstract

Graph theory is an applied branch of mathematics which deals with problems with the help of graphs. One of the popular areas of research in graph theory is the study of the graphs that are obtained from given graphs. Concept of total graph comes under this category. Every graph has a total graph but all graphs are not total graphs of some graph. The total graph T(G) of G is the graph whose vertex set corresponds to the set of vertices and edges of G such that two vertices of T(G) are adjacent if and only if the corresponding elements of G are adjacent or incident. This paper gives formulas to find the regularity, the number of triangles and the number of edges of total graphs of certain standard graphs like path graph, complete graph cyclic graph.

Key concepts: Combinatorics, Symmetric graph, Mathematics, Line graph, Block graph, Discrete mathematics, Pathwidth, Cograph

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