Abstract
In this paper, by means of the degree sequences (DS) of graphs and some graph theoretical and combinatorial methods, we determine the algebraic structure of the set of simple connected graphs according to two graph operations, namely join and Corona product. We shall conclude that in the case of join product, the set of graphs forms an abelian monoid whereas in the case of Corona product, this set is not even associative, it only satisfies two conditions, closeness and identity element. We also give a result on distributive law related to these two operations.
Highlights
Received 2017-11-27; accepted 2018-02-01; published 2018-11-02. 2010 Mathematics Subject Classification. 05C07, 05C10, 05C30, 05C76
By means of the degree sequences (DS) of graphs and some graph theoretical and combinatorial methods, we determine the algebraic structure of the set of simple connected graphs according to two graph operations, namely join and Corona product
We give a result on distributive law related to these two operations
Summary
Received 2017-11-27; accepted 2018-02-01; published 2018-11-02. 2010 Mathematics Subject Classification. 05C07, 05C10, 05C30, 05C76. By means of the degree sequences (DS) of graphs and some graph theoretical and combinatorial methods, we determine the algebraic structure of the set of simple connected graphs according to two graph operations, namely join and Corona product.
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