creative_2015_24_1_089_095_001

kk-Combinations of an unlabelled graph


M. R. Ebrahimi VishkiK. MirzavaziriM. Mirzavaziri


Abstract

creative_2015_24_1_089_095_abstract

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creative_2015_24_1_089_095

In this paper we extend the notion of the binomial coefficient (nk)(nk) into a new notion ([G]k)([G]k), where [G][G] is an unlabelled graph with nn vertices and 0⩽k⩽n0⩽k⩽n. We call ([G]k)([G]k) as the graph binomial coefficient and a version of the graph binomial expansion is also studied. As an application of this notion, we enumerate the number of ways to color vertices of a path and beads of a necklace.

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Author(s)

Ebrahimi Vishki, M. R., Mirzavaziri, K., Mirzavaziri, M.