Geodesic
Spectrum of two new joins of graphs and infinite families of integral graphs
Kragujevac Journal of Mathematics, Tome 36 (2012) no. 1, p. 133

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $G_1$ and $G_2$ be two graphs with $V(G_1)=\{u_1,u_2,\dots,u_{n_1}\}$, $E(G_1)=\{e_1,e_2,\dots,e_{m_1}\}$ and $V(G_2)=\{v_1,v_2,\dots,v_{n_2}\}$. Let $ S(G) $ denote the subdivision graph of $G$ [3]. The $S_{vertex}$ join of $G_1$ with $G_2$, denoted by $ G_1 \veedot G_2$ is obtained from $S(G_1) $ and $G_2$ by joining all vertices of $G_1$ with all vertices of $G_2$. The $S_{edge}$ join of $G_1$ with $G_2$, denoted by $ G_1 \veebar G_2$ is obtained from $S(G_1) $ and $G_2$ by joining all vertices of $S(G_1)$ corresponding to the edges of $G_1$ with all vertices of $G_2$. In this paper we obtain the spectrum of these two new joins of graphs. As an application some infinite family of new classes of integral graphs are constructed.
Classification : 05C 05C12
Keywords: Adjacency matrix, Characteristic Polynomial, Join of graphs 
@article{KJM_2012_36_1_a13,
     author = {Gopalapillai Indulal},
     title = {Spectrum of two new joins of graphs and infinite families of integral graphs},
     journal = {Kragujevac Journal of Mathematics},
     pages = {133 },
     publisher = {mathdoc},
     volume = {36},
     number = {1},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2012_36_1_a13/}
}
TY  - JOUR
AU  - Gopalapillai Indulal
TI  - Spectrum of two new joins of graphs and infinite families of integral graphs
JO  - Kragujevac Journal of Mathematics
PY  - 2012
SP  - 133 
VL  - 36
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2012_36_1_a13/
LA  - en
ID  - KJM_2012_36_1_a13
ER  - 
%0 Journal Article
%A Gopalapillai Indulal
%T Spectrum of two new joins of graphs and infinite families of integral graphs
%J Kragujevac Journal of Mathematics
%D 2012
%P 133 
%V 36
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2012_36_1_a13/
%G en
%F KJM_2012_36_1_a13
Gopalapillai Indulal. Spectrum of two new joins of graphs and infinite families of integral graphs. Kragujevac Journal of Mathematics, Tome 36 (2012) no. 1, p. 133 . http://geodesic.mathdoc.fr/item/KJM_2012_36_1_a13/