In this paper, we investigate domination number as well as signed domination numbers of Cay(G : S) for all cyclic group G of order n, where n in {p^m; pq} and S = { a^i : i in B(1; n)}. We also introduce some families of connected regular graphs gamma such that gamma_S(Gamma) in {2,3,4,5 }.

‎In the present study‎, ‎we consider a regular curve in Galilean‎ ‎$4$-space $mathbb{G}_{4}$ whose position vector is written as a‎ ‎linear combination of its Frenet vectors‎. ‎We characterize such‎ ‎curves in terms of their curvature functions‎. ‎Further‎, ‎we obtain‎ ‎some results of rectifying‎, ‎constant ratio‎, ‎$T$-constant and‎ ‎$N$-constant curves in $mathbb{G}_{4}$‎.

By Seidel’s switching, we construct new strongly regular graphs with parameters (276, 140, 58, 84). In this paper, we simplify the known switching theorem due to Bose and Shrikhande as follows. Let G = (V,E) be a primitive strongly regular graph with parameters (v, k, λ, μ). Let S(G,H) be the graph from G by switching with respect to a nonempty H ⊂ V . Suppose v = 2(k − θ1) where θ1 is the nont...

A b-coloring of a graph is a proper coloring such that every color class contains a vertex adjacent to at least one vertex in each of the other color classes. The b-chromatic number of a graph G, denoted by b(G), is the maximum integer k such that G admits a b-coloring with k colors. El Sahili and Kouider conjectured that b(G) = d + 1 for d-regular graph with girth 5, d ≥ 4. In this paper, we p...

Given a set of integers S; G(S) = (S; E) is a graph, where the edge uv exists if and only if u+ v∈ S. A graph G = (V; E) is an integral sum graph or ISG if there exists a set S ⊂ Z such that G=G(S). This set is called a labeling of G. The main results of this paper concern regular ISGs. It is proved that all 2-regular graphs with the exception of C4 are integral sum graphs and that for every po...

The circular ow number F c (G) of a graph G = (V; E) is the minimum r 2 Q such that G admits a ow with 1 (e) r ? 1, for each e 2 E. We determine the circular ow number of some regular multigraphs. In particular, we characterize the bipartite (2t + 1)-regular graphs (t 1). Our results imply that there are gaps for possible circular ow numbers for (2t + 1)-regular graphs, e.g. there is no cubic g...

We have previously introduced vertex attack tolerance (VAT), denoted mathematically as τ(G) = minS⊂V |S| |V−S−Cmax(V−S)|+1 where Cmax(V −S) is the largest connected component in V − S, as an appropriate mathematical measure of resilience in the face of targeted node attacks for arbitrary degree networks. A part of the motivation for VAT was the observation that, whereas conductance, Φ(G), captu...

Let G be a 2r-regular, 2r-edge-connected graph of odd order and let m be an integer such that 1 ~ m ~ r 1. For any vertex u of G, the graph G {u} has an m-factor which contains none of r m given edges. All graphs considered are finite. We shall allow graphs to contain multiple edges and we refer the reader to [2] for graph theoretic terms not defined in this paper. Let G be a graph. We denote b...

The orbit projection π :M →M/G of a proper G-manifold M is a fibration if and only if all points inM are regular. Under additional assumptions we show that π is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: π is a G-quasifibration if and only if all points are regular.

Let G be a simple undirected graph. The regular number of G is defined to be the minimum number of subsets into which the edge set of G can be partitioned so that the subgraph induced by each subset is regular. In this work, we obtain the regular number of some families of graphs and discuss some general bounds on this parameter. Also, some of the lower or upper bounds proved in [4] are shown h...