Journal of Interconnection Networks

Water has covered a wide part of the earth’s surface. Oceans and other water bodies contain significant natural and environmental resources as well as aquatic life. Due to humans’ hazardous and unsuitable underwater (UW) settings, these are generally undiscovered and unknown. As a result of its widespread utility in fields as diverse as oceanography, ecology, seismology, and oceanography, underwater wireless sensor networks (UWSNs) have emerged as a cutting-edge area of study. Despite their usefulness, the performance of the network is hampered by factors including excessive propagation delay, a changing network architecture, a lack of bandwidth, and a battery life that is too short on sensor nodes. Developing effective routing protocols is the best way to overcome these challenges. An effective routing protocol can relay data from the network’s root node to its final destination. Therefore, the state of the art in underwater wireless acoustic sensor network (UWASN) routing protocols is assessed with an eye toward their potential for development. In real-world applications, sensor node positions are frequently used to locate relevant information. As a result, it is crucial to conduct research on routing protocols. Reinforcement learning (RL) algorithms have the ability to enhance routing under a variety of conditions because they are experience-based learning algorithms. Underwater routing methods for UWSN are reviewed in detail, including those that rely on machine learning (ML), energy, clustering and evolutionary approaches. Tables are incorporated for the suggested protocols by including the benefits, drawbacks, and performance assessments, which make the information easier to digest. Also, several applications of UWSN are discussed with security considerations. In addition to this, the analysis of node deployment and residual energy is discussed in this review. Furthermore, the domain review emphasizes UW routing protocol research difficulties and future directions, which can help researchers create more efficient routing protocols based on ML in the future.

Let $G$ be a graph. A set $W(\subseteq V(G))$ is a local resolving set of $G$ if there exists $w\in W$ such that $d_G(w,v)\ne d_G(w,u)$ for any $uv\in E(G)$. The local metric dimension ${\mathrm{\text{dim}}}_{\ell }(G)$ of $G$ is the minimum cardinality of all the local resolving sets of $G$. In this paper, we characterize the graphs with ${\mathrm{\text{dim}}}_{\ell }(G)=2$. Next, we obtain the Nordhaus–Gaddum-type results for local metric dimension. Finally, the local metric dimension of several graph classes is given.

The proper rainbow vertex connection number of $G$, denoted by $prvc(G)$, is the smallest number of colors needed to properly color the vertices of $G$ to make $G$ rainbow vertex connected. The proper strong rainbow vertex connection number of $G$, denoted by $psrvc(G)$, is the smallest number of colors needed to properly color the vertices of $G$ to make $G$ strong rainbow vertex connected. These two concepts are inspired by the concepts of proper (strong) rainbow connection number of graphs. In this paper, we determine the values of $prc(G)$ and $psrc(G)$ of $G$ with large clique numbers $n-1$ and $n-2$. Moreover, we determine the values of $prvc(G)$ and $psrvc(G)$ of $G$ with large clique numbers $n-1$, $n-2$ and $n-3$.

We make the source network load storage access power wireless private network, this paper proposes a source network load storage access power wireless private network technology based on 5G ultra dense network. The multiple rotation scheduling and self-organizing learning methods are used to establish the deployment model of the source network load storage access node of the power wireless private network under the 5G communication mode. According to the routing control algorithm design of the 5G ultra dense networking node, combined with the integration analysis of the access load parameters, the source network load storage access model of the 5G ultra dense networking under the dynamic load distributed control mode is established. Through the method of optimal control of reactive power and voltage of distribution network, the transmission link equilibrium structure model of 5G source network load storage access to power wireless private network is constructed. Combined with the coverage analysis of link topology structure and the benefit maximization constraint analysis of production and consumption users, the active and reactive capacity analysis of transaction between production and consumption user groups and multiple production and consumption users is adopted. Combined with the energy storage characteristics analysis and power flow parameter calculation of the source network load storage access power, the 5G ultra dense networking and private network access to the source network load storage access power are realized. The test shows that this method has better power balance dispatching ability and larger output power gain when it is applied to the design of source network load storage access power wireless private network.

Finding the values of $A(n,d)$ and $A(n,d,w)$ is a fundamental problem in classical coding theory. The $A(n,d,w)$ is the size of the maximum independent set of $Q_n^{(d-1,w)},$ which is the induced subgraph of vectors of weight $w$ of the $(d-1)\mathrm{\text{th}}$-power of $n$-dimensional hypercubes. Obviously, $A(n,d,w)=\alpha (Q_n^{(d-1,w)})$. In order to further understand and study the independent set of $Q_n^{(d-1,w)}$, we explore its clique number and the structure of the maximum clique. In this paper, we obtain the clique number and the structure of the maximum clique of $Q_n^{(d,w)}$ for $6\le d\le 7.$ As an application, by $\alpha (G)w(G)\le |V(G)|,$ we obtain the upper bounds of $A(n,d,w)$ for $7\le d\le 8.$

The line graph is a very popular research object in graph theory, in complex networks and also in social networks recently. Let $L(K_{m,n})$ be the line graph of the complete bipartite graph $K_{m,n}$ and $P_{k+1}$ be a path of length $k$. In this paper, we give necessary and sufficient conditions for the existence of $P_4$-decompositions of $L(K_{m,n})$.

Motivated by the problem of network monitoring, Foucaud, Krishna and Ramasubramony Sulochana introduced the concept of monitoring edge-geodetic set and a related graph invariant. A monitoring edge-geodetic set (MEG-set for short) is a set such that the removal of any edge changes the distance between some pair of vertices in the set. The minimum size of the monitoring edge-geodetic set is called the monitoring edge-geodetic number. In this paper, we study the monitoring edge-geodetic numbers of some well-known networks, including folded hypercube, folded $n$-cube, prism graph, anti-prism graph, Jahangir graph and windmill graphs.

Let $c$ be a red–white coloring of the vertices of a nontrivial connected graph $G$ with diameter $d$, where at least one vertex is colored red. Then $c$ is called an identification coloring or simply, an ID-coloring, if and only if for any two vertices $u$ and $v$, $\overrightarrow{d}(u)\ne \overrightarrow{d}(v)$, where for any vertex $w$, $\overrightarrow{d}(w)=(a_1,a_2,\dots ,a_d)$ and $a_i$ is the number of red vertices at a distance $i$ from $w$. A graph is said to be an ID-graph if it possesses an ID-coloring. If $G$ is an ID-graph, then the spectrum of $G$ is the set of all positive integers $r$ for which $G$ has an ID-coloring with $r$ red vertices. The identification number or ID-number of a graph is the smallest element in its spectrum. In this paper, we extend a result of Kono and Zhang on the identification number of grids $P_m\square P_n$. In particular, we give a formulation of strong ID-coloring and use it to give a sufficient condition for an ID-coloring of a graph to be extendable to an ID-coloring of the Cartesian product of a path $P_m$ with $G$. Consequently, some elements of the spectrum of grids $P_m\square P_n$ for positive integers $m$ and $n$, with $n\ge 4$, are obtained. The complete spectrum of ladders $P_2\square P_n$ is then determined using systematic constructions of ID-colorings of the ladders.

Graph embedding is a fundamental problem in computer science. Let $H$ (resp., $G$) be the interconnection network for a parallel computer system $S_H$ (resp., $S_G$). If $G$ could be embedded into $H$, then $S_H$ can simulate $S_G$’s behavior. The $k$-ary $n$-cube $Q_n^k$ is a node-symmetric and link-symmetric recursive interconnection network for parallel computer systems. Let $L$ be a prescribed linear forest of $Q_n^k$, and let $u$ and $v$ be any two distinct nodes in $Q_n^k$ such that $L$ has no path with $u$ or $v$ as internal nodes, or both as end-nodes. This paper shows that there is a Hamiltonian path passing through $L$ between $u$ and $v$ in $Q_n^k$ with $n\ge 2$ and odd $k\ge 5$ even if the number of links in $L$ is up to $2n-2$.

The exact deg-centric graph of a simple, connected graph $G$, denoted by $G_{\mathrm{\text{ed}}}$, is a graph constructed from $G$ such that $V(G_{\mathrm{\text{ed}}})=V(G)$ and $E(G_{\mathrm{\text{ed}}})=\{v_i{v}_j:d_G(v_i,v_j)={\mathrm{\text{deg}}}_G(v_i)\}$. In this paper, the concepts of exact deg-centric graphs and iterated exact deg-centrication of a graph are introduced and discussed.