Abstract

For the finite graph $G=(V,E)$. A book graph $B_n$ taken as follows. $V(B_n)=\{u_1,~ u_2\}\bigcup \{v_i,~ w_i ~/~ 1 \leq i \leq n\}$ and $E(B_n)=\{e_1=u_1u_2\} \bigcup \{e^{'}_{j}= u_1v_j,~~ e^{''}_{j}= u_2w_j,~~ e^{'''}_{j}= v_j w_j ~/~ 1 \leq j \leq n\}$. We consider the generalized book graph $B_{n,m}$ with vertex and edge sets by $V(B_{n,m})=\{u_i ~ / ~ 1 \leq i \leq m-2\} \bigcup \{v_i,~ w_i ~/\break 1\leq i \leq n \}$ and $E(B_{n,m})= \{e_i=u_i u_{i+1} ~/~ 1\leq i \leq m-3\} \bigcup \{e^{'}_{j}= u_1v_j, ~~ e^{''}_{j}= u_{m-2} w_j, ~~ e^{'''}_{j}=v_j w_j ~/~ 1 \leq j \leq n \}$. This report investigates the decomposition of book graph $B_n$ and generalized book graph $B_{n,m}$.

Keywords and Phrases

Generalized book graph, Book graph, Decomposition, stars, cycles, paths.

A.M.S. subject classification

05C70.

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