Journal of Discrete Mathematics and Its Applications
https://jdma.sru.ac.ir/
Journal of Discrete Mathematics and Its Applicationsendaily1Fri, 01 Dec 2023 00:00:00 +0330Fri, 01 Dec 2023 00:00:00 +0330A generalized version of symmetric division degree index
https://jdma.sru.ac.ir/article_2072.html
The symmetric division degree $SDD$-index of a simple connected graph $G$ is defined as the sum of terms $f(d_u,d_v)=(d_u/d_v)+(d_v/d_u)$ over all pairs of distinct adjacent vertices of $G$; where $d_u$ denotes the degree of a vertex $u$ of graph $G$. In this paper, we introduce the general form of symmetric division degree index by replacing the degree of vertices $f(d_u,d_v)$ with another symmetric function of vertex properties. We establish some properties of the generalized symmetric division degree index $GSDD$ index for certain special functions and calculate the values of these new indices for some well-known graphs.Perfect State Transfer on Cayley Graphs over Groups
https://jdma.sru.ac.ir/article_2073.html
Perfect state transfer (\textit{PST}) on graphs due to their significant applications in quantum information processing and quantum computations. In the present work, we establish a characterization of Cayley graphs over $U_{6n}$ group, having \textit{PST}.Spectral Properties of Fullerene Graphs
https://jdma.sru.ac.ir/article_2077.html
Fullerenes are polyhedral molecules made of carbon atoms. They&nbsp;have attracted much attention in the chemical and the mathematical literature.In the present paper, we investigate problems concerned with the eigenvalues of fullerene graphs. We obtain new upper bounds for the smallest eigenvalues of fullerenes using bipartite edge-frustration of their related subgraphs.