# A-polynomial for some family of caveman graphs

## DOI:

https://doi.org/10.56947/amcs.v18.196## Keywords:

Clique, Caveman graphs, A-polynomial## Abstract

The caveman graph is a graph formed by modifying a set of isolated *k*-cliques (or caves) by removing one edge from each clique and using it to connect to a neighboring clique along a central cycle such that all *n* cliques form a single unbroken loop. Caveman graph containing *n*-copies of k-cliques is denoted as, *(n,k)*-caveman graph. For a graph *G*, the *A*-matrix is defined as, *A(G)=[a _{ij}] *in which

*a*if vertices

_{ij}=1*v*and

_{i}*v*are adjacent; and

_{j}*0*otherwise. The polynomial associated with

*A*-matrix is the

*A*-polynomial. In this work, we study

*A*-polynomial for some family of caveman graphs.

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