The generalized hierarchical product of graphs
نویسندگان
چکیده
منابع مشابه
The generalized hierarchical product of graphs
A generalization of both the hierarchical product and the Cartesian product of graphs is introduced and some of its properties are studied. We call it the generalized hierarchical product. In fact, the obtained graphs turn out to be subgraphs of the Cartesian product of the corresponding factors. Thus, some well-known properties of this product, such as a good connectivity, reduced mean distanc...
متن کاملWeighted Szeged Index of Generalized Hierarchical Product of Graphs
The Szeged index of a graph G, denoted by S z(G) = ∑ uv=e∈E(G) nu (e)n G v (e). Similarly, the Weighted Szeged index of a graph G, denoted by S zw(G) = ∑ uv=e∈E(G) ( dG(u)+ dG(v) ) nu (e)n G v (e), where dG(u) is the degree of the vertex u in G. In this paper, the exact formulae for the weighted Szeged indices of generalized hierarchical product and Cartesian product of two graphs are obtained.
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A new operation on graphs is introduced and some of its properties are studied. We call it hierarchical product, because of the strong (connectedness) hierarchy of the vertices in the resulting graphs. In fact, the obtained graphs turn out to be subgraphs of the cartesian product of the corresponding factors. Some well-known properties of the cartesian product, such as a reduced mean distance a...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.10.028