Let G = (V(G), E(G)) be a connected graph and d(f, y) denotes the distance between edge f vertex y, which is defined as min{d(p, y), d(q, y)}, where y).An metric generator with minimum number of vertices called an basis for cardinality dimension represented by edim(G).In this paper, we study flower n×3 also calculate prism related graphs D n t .It has been concluded that bounded, while unbounded.

Consider an undirected and connected graph G = ( V , E ) where represent the set of vertices edges respectively. The concept edge version metric dimension doubly resolving sets is based on distances in a graph. In this paper, we find for necklace

Topological indices are numerical parameters associated with underlying topology of a molecular structure. They correlated several physio-chemical properties chemical compounds. Recently, Euclidean metric based topological index has been introduced named as Sombor index. Therefore, in this article, we will discuss combinatorial aspects and compute index, average the reduced line graph silicate carbides Si2C3-I[p, q].

We study the Betti numbers of binomial edge ideal associated to some classes graphs with large Castelnuovo-Mumford regularity. As an application we give several lower bounds regularity arbitrary depending on induced subgraphs.

Abstract In this paper, we compute first Zagreb index (coindex), second third index, hyper-Zagreb atom-bond connectivity fourth sum Randić augmented Sanskruti geometric-arithmetic and fifth of the line graphs Banana tree graph Firecracker graph.

Let $W_E = \{w_1, w_2, \ldots, w_k\}$ be an ordered set of vertices graph $G$ and let $e$ edge $G$. Suppose $d(x, e)$ denotes distance between vertex $x$ $G$, defined as $d(e, x) d(x, e) \min \{d(x, a), b)\}$, where $e ab$. A distinguishes two edges $e_1$ $e_2$, if $d(e_1, x)\neq d(e_2, x)$. The representation $r(e\mid W_E)$ with respect to $W_E$ is the k-tuple $(d(e, w_1), d(e, w_2), w_k))$. If distinct have $W_E$, then called metric generator for An minimum cardinality basis its dimension...

In this paper, we give theoretical results for some topological indices such as Zagreb , co-indices hyper-Zagreb index HM(G), atom-bond connectivity ABC(G), sum (G) and geometric-arithmetic GA(G), by considering G line graph of subdivision convex polytopes denotes its complement.

The partition dimension is a variant of metric in graphs. It has arising applications the fields network designing, robot navigation, pattern recognition and image processing. Let G (V (G) , E (G)) be connected graph Γ = {P1, P2, …, Pm} an ordered m-partition V (G). representation vertex v with respect to m-vector r (v|Γ) (d (v, P1) d P2) Pm)), where P) min {d x) |x ∈ P} distance between P. If m-vectors differ at least 2 positions for all (G), then called 2-partition generator G. A minimum...

Abstract In this paper, we study 3–total edge product cordial (3–TEPC) labeling which is a variant of labeling. We discuss Web, Helm, Ladder and Gear graphs in context 3–TEPC also some particular examples with corona graph.

In this paper, we introduce new labeling and named it as k-total edge mean cordial (k-TEMC) labeling.We study certain classes of graphs namely path, double comb, ladder fan in the context 3-TEMC labeling.

Fault-tolerant resolving partition is natural extension of partitions which have many applications in different areas computer sciences for example sensor networking, intelligent systems, optimization and robot navigation. For a nontrivial connected graph G (V (G) , E (G)), the representation vertex v with respect to an ordered Π = {Si : 1 ≤ i k} V k-vector r ( | ) d S k where, (v, Si) min {d x) |x ∈ Si}, {1, 2, …, k}. A said be fault-tolerant set if (u|Π) (v|Π) differ by at least two places...

In this paper, we introduce the edge version of doubly resolving set a graph which is based on distances graph. As main result, computed minimum cardinality \(\psi_E\) sets family \(n\)-sunlet \(S_n\) and prism \(Y_n\).

Monitoring and controlling complex networks is of great importance to understand different types technological physical systems for source localization. Source localization refers the process determining location or position a signal in space based on measurements obtained from multiple sensors. Doubly resolving sets, also known as doubly-resolving arrays, are particular type sensor configuration that can enhance accuracy In other words, network equivalent calculating minimal doubly sets...

Locating the source of diffusion in complex networks is an exciting but challenging task. It critical for preventing and controlling epidemic risks. Source localization has been studied under many feasible models. In this paper, we discuss problem Kayak paddle graphs [Formula: see text] by computing edge version metric double dimensions.

Fault tolerance is the characteristic of a system that permits it to carry on its intended operations in case failure one units. Such known as fault-tolerant self-stable system. In graph theory, if we remove any vertex resolving set, then resulting set also called and minimum cardinality metric dimension. this paper, determine resolvability line graphs. As main result, computed dimension graphs necklace prism (2010 Mathematics Subject Classification: 05C78).

The field of graph theory is extensively used to investigate structure models in biology, computer programming, chemistry, and combinatorial optimization. In order work with the chemical structure, chemists require a mathematical form compound. can be depicted using nodes (which represent atom) links many types bonds). As result, theoretic explanation this problem give representations for such that different have unique representations. This study referred as metric dimension. article, we...

Topological indices correlate certain physicochemical properties like boiling point, stability, and strain energy of chemical compounds. In this report, we compute M-polynomials for PAMAM dendrimers polyomino chains. Moreover, by applying calculus, nine important topological under-study

The suppression of harmful information and even its diffusion can be predicted delayed by precisely finding sources with limited resources. doubly resolving sets (DRSs) play a crucial role in determining where occurs network. Source detection problems are among the most challenging exciting complex networks. This problem has great significance controlling any outbreak. virus source network is basically locating node that spreads observed diffusion. solved using connection to well-known...

Abstract Let G = ( V ), E )) be a connected graph and x, y ∈ d ) min{ length of x − path } for e b )}, where ab . A vertex distinguishes two edges 1 2 , if ≠ ). W { w ., k an ordered set in let The representation r | with respect to is the -tuple e, )). If distinct have then called edge metric generator An minimum cardinality basis its dimension denoted by edim( circulant C n (1, m has v i +1 : ≤ n− 1}∪{ }∪{ i+m n−m n−m+i }. In this paper, it shown that graphs 2) 3) constant.

A source detection problem in complex networks has been studied widely. Source localization much importance order to model many real-world phenomena, for instance, spreading of a virus computer network, epidemics human beings, and rumor on the internet. is identify node network that gives best description observed diffusion. For this purpose, we select subset nodes with least size such can be uniquely located. This equivalent find minimal doubly resolving set network. In article, have...

Source localization is one of the most challenging problems in complex networks. Monitoring and controlling networks great interest for understanding different types systems, such as biological, technological, physical systems. Modern research has made developments identifying sensors through which we can monitor or control For this task, choose a set with smallest possible size so that source may be identified. The problem locating an epidemic network equivalent to finding minimal doubly...

Locating the sources of information spreading in networks including tracking down origins epidemics, rumors social networks, and online computer viruses, has a wide range applications. In many situations, identifying where an epidemic started, or which node network served as source, is crucial. But it can be difficult to determine root outbreak, especially when data are scarce noisy. The goal find source infection by analysing provided only limited number observers, such nodes that indicate...