The aim of Open Journal of Discrete Applied Mathematics (ODAM) (2617-9687 Online, 2617-9679 Print) is to bring together research papers in different areas of algorithmic and applied mathematics as well as applications of mathematics in various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. To ensure fast publication, editorial decisions on acceptance or otherwise are taken within 4 to 12 weeks (three months) of receipt of the paper.
Accepted articles are immediately published online as soon as they are ready for publication. There is one volume containing three issues per year. The issues will be finalized in April, August, and December of every year. The printed version will be published in December of every year.
For an undirected graph \(G\), a zero-sum flow is an assignment of nonzero integers to the edges such that the sum of the values of all edges incident with each vertex is zero, and we call it a zero-sum \(k\)-flow if the absolute values of edges are less than \(k\). We define the zero-sum flow number of \(G\) as the least integer \(k\) for which \(G\) admitting a zero sum \(k\)-flow. In this paper we gave complete zero-sum flow and zero sum number for octagonal grid, generalized prism and book graph.
Let \(V(G) = \{v_1, v_2, \ldots, v_n\}\) be the vertex set of \(G\) and let \(d_{G}(v_i)\) be the degree of a vertex \(v_i\) in \(G\). The degree subtraction adjacency matrix of \(G\) is a square matrix \(DSA(G)=[d_{ij}]\), in which \(d_{ij}=d_{G}(v_i)-d_{G}(v_j)\), if \(v_i\) is adjacent to \(v_j\) and \(d_{ij}=0\), otherwise. In this paper we express the eigenvalues of the degree subtraction adjacency matrix of subdivision graph, semitotal point graph, semitotal line graph and total graph of a regular graph in terms of the adjacency eigenvalues of \(G\). Further we obtain the degree subtraction adjacency energy of these graphs.
The zeroth-order general Randić index of a simple connected graph G is defined as \(R_{\alpha}^{0}(G)=\sum_{u\in V(G)} \big(d(u)\big)^{\alpha}\), where \(d(u)\) is the degree of \(u\) and \(\alpha\not\in \{0,1\}\) is a real number. A \(k\)-polygonal cactus is a connected graph in which every edge lies in exactly one cycle of length \(k\). In this paper, we present the extremal \(k\)-polygonal cactus with \(n\) cycles for \(k\geq3\) with respect to the zeroth-order general Randić index.
