Advances and Applications in Discrete Mathematics
Volume 35, , Pages 77 - 85
(November 2022) http://dx.doi.org/10.17654/0974165822053 |
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CLIQUE COMMON NEIGHBORHOOD POLYNOMIAL OF GRAPHS
Rosalio G. Artes, Jr., Mercedita A. Langamin and Almira B. Calib-og
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Abstract: Let G be a simple connected graph of order at least 2. An i-subset of is a subset of of cardinality i. An i-clique is an i-subset which induces a complete subgraph of G. The clique common neighborhood polynomial of G is given by where is the number of i-cliques in G with common neighborhood cardinality equal to j and is the cardinality of a maximum clique in G, called the clique number of G. In this paper, we established the clique common neighborhood polynomials of the special graphs such as the complete graph, complete bipartite graph and complete q-partite graph. Moreover, we have shown that the clique polynomial is a special evaluation of the clique common neighborhood polynomial at
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Keywords and phrases: clique, clique polynomial, clique common neighborhood polynomial |
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