Flower Graph Research Articles

Mean Distance on Metric Graphs

We introduce a natural notion of mean (or average) distance in the context of compact metric graphs, and study its relation to geometric properties of the graph. We show that it exhibits a striking number of parallels to the reciprocal of the spectral gap of the graph Laplacian with standard vertex conditions: it is maximised among all graphs of fixed length by the path graph (interval), or by the loop in the restricted class of doubly connected graphs, and it is minimised among all graphs of fixed length and number of edges by the equilateral flower graph. We also establish bounds for the correctly scaled product of the spectral gap and the square of the mean distance which depend only on combinatorial, and not metric, features of the graph. This raises the open question whether this product admits absolute upper and lower bounds valid on all compact metric graphs.

Enumeration of spanning trees in prisms of some graphs

In graph theory, a prism over a graph G is the cartesian product of the graph G with P₂. The purpose of this work is to investigate the complexity of the prisms of some path and cycle-related graphs. In particular, we obtain simpler and more explicit formulas for the complexity of a special class of prisms of path-related graphs: fan graph, ladder graph, the composition Pn[P₂] graph, and book graph. Moreover, we obtain straightforward formulas for the complexity of a special class of prisms of cycle-related graphs: wheel graph, gear graph, prism graph, n−crossed prism graph, mirror graph M(Cn) of even cycle Cn, twisted prism, total graph T(Cn) of the cycle Cn, the friendship graph, the flower graph, and planner sunflower graph. These closed formulas are deduced using some basic properties of block matrix, recurrence relation, eigenvalues of circulant matrices, and orthogonal polynomials.

On H-irregular reflexive labeling of graph

By an irregular reflexive labeling, we mean a function and such that if and if , where max . Let , the irregular reflexive labeling is called an -irregular reflexive -labeling of graph if every two different sub graphs and isomorphic to , it holds , where . The minimum for graph which has an -irregular reflexive -labeling is called the reflexive strength of graph and denoted by . In this paper we initiate to study the lower bound of the reflexive strenght of graphs and the reflexive strenght of flower, Shack and book graph, where isomorphic to and , respectively.

Some Results On Total Onto Minus Edge Dominating Functions In Graphs

Let G = (V, E) be a graph. The total onto minus edge dominating function is a function f: E → {−1, 0, 1} such that f is onto and f (N(e)) ≥ 1 for all e ∈ E(G). The total onto minus edge domination number of a graph G is a minimum weight of a set of all total onto minus edge dominating functions of G and it is denoted by .
 In this paper we discuss about the total onto minus edge domination number for some graphs : Star graph, Bistar graph, Friendship graph and Flower graph.

Fuzzy Computational Analysis of Flower Graph via Fuzzy Topological Indices

Fuzzy graphs have many applications not only in mathematics but also in any field of science where the concept of fuzziness is involved. The notion of fuzziness is suitable in any environment, which favor to predicts the problem and solve this problem in a decent way. As compared to crisp theory, fuzzy graphs are a more beneficial and powerful tool to get better accuracy and precision due to their fuzziness property. A topological index is a numerical value which characterizes the properties of the graph. Topological indices were basically developed for chemical structures, but these are also used for general graphs as well. In chemical graph theory, topological indices are used to extract the chemical properties of the graphs. These indices are also well studied in fuzzy environment. Applications of fuzzy graphs are found in medicines, telecommunications, traffic light control, and many more. Our aim is to find these fuzzy topological indices for flower graphs to strengthen the concepts of fuzziness in general graphs. In this paper, some novel results for f m × r flower graphs are achieved.

On the study of Rainbow Antimagic Coloring of Special Graphs

Let be a connected graph with vertex set and edge set . The bijective function is said to be a labeling of graph where is the associated weight for edge . If every edge has different weight, the function is called an edge antimagic vertex labeling. A path in the vertex-labeled graph , with every two edges satisfies is said to be a rainbow path. The function is called a rainbow antimagic labeling of , if for every two vertices , there exists a rainbow path. Graph admits the rainbow antimagic coloring, if we assign each edge with the color of the edge weight . The smallest number of colors induced from all edge weights of edge antimagic vertex labeling is called a rainbow antimagic connection number of , denoted by . In this paper, we study rainbow antimagic connection numbers of octopus graph , sandat graph , sun flower graph , volcano graph and semi jahangir graph Jn.

TOTAL DOMINATION INTEGRITY OF WHEEL RELATED GRAPHS

The total domination integrity of a simple connected graph G with no isolated vertices is denoted by TDI(G) and defined as TDI(G)=min { left | S right |+m(G-S) : S subseteq V(G) }, where S is a total dominating set of G and m(G - S) is the order of a maximum connected component of G - S. It is a new measure of vulnerability of a graph. This work is aimed to discuss total domination integrity of wheel, gear, helm, closed helm, flower graph, web graph, sunflower graph and web graph without center.

一类花图对应链环的Jones多项式

一类花图对应链环的Jones多项式

Applying the (1,2)-pitchfork domination and it's inverse on some special graphs

Let G be a finite simple and undirected graph without isolated vertices. For any non-negative integers j and k, a subset D of V is called a pitchfork dominating set if every vertex in D dominates at least j and at most k vertices of V - D. A subset D -1 of V - D is an inverse pitchfork dominating set if it is a dominating set. The pitchfork domination number of G, denoted by pf (G) is a minimum cardinality over all pitchfork dominating sets in G. The inverse pitchfork domination number of G, denoted by pf-1 (G) is a minimum cardinality over all inverse pitchfork dominating sets in G. In this paper, pitchfork dominations and it's inverse are applied when j = 1 and k = 2 on some standard graphs such as: tadpole graph, lollipop graph, lollipop flower graph , daisy graph and Barbell graph.

On local edge antimagic chromatic number of graphs

Let G = (V,E) be a graph of order p and size q having no isolated vertices. A bijection f : V → {1, 2, 3, ..., p} is called a local edge antimagic labeling if for any two adjacent edges e = uv and e’ = vw of G, we have w(e) ≠ w(e’), where the edge weight w(e = uv) = f(u)+f(v) and w(e’) = f(v)+f(w). A graph G is local edge antimagic if G has a local edge antimagic labeling. The local edge antimagic chromatic number χ’lea(G) is defined to be the minimum number of colors taken over all colorings of G induced by local edge antimagic labelings of G. In this paper, we determine the local edge antimagic chromatic number for a friendship graph, wheel graph, fan graph, helm graph, flower graph, and closed helm.

On Computing Techniques for Sombor Index of Some Graphs

In all types of topological indicators, degree-based indicators play a major role in chemical graph theory. The topological index is a fixed numeric value associated with graph isomerism. Firstly, in 1972, the concept of degree-based index was developed by Gutman and Trinajstic. These degree-based indices are divided into two ways, namely, degree and connection number. These degree-based graph indices are positive-valued for non-regular graphs and zero for regular graphs. In this article, we discussed the degree-based Sombor, reduced Sombor, and average Sombor indices for wheel graph, gear graph, helm graph, flower graph, sunflower graph, and lobster graph.

NM-polynomials and Topological Indices of Some Cycle-Related Graphs

Topological indices (molecular descriptors) are numerical values of a chemical structure and represented by a graph. Molecular descriptors are used in QSPR/QSAR modeling to determine a chemical structure’s physical, biological, and chemical properties. The cycle graphs are symmetric graphs for any number vertices. In this paper, recently defined neighborhood degree sum-based molecular descriptors and polynomials are studied. NM-polynomials and molecular descriptors of some cycle-related graphs, which consist of the wheel graph, gear graph, helm graph, flower graph, and friendship graph, are computed and compared.

BILANGAN INVERS DOMINASI TOTAL PADA GRAF BUNGA DAN GRAF TRAMPOLIN

Given a simple, finite, undirected and contains no isolated vertices graph , with is the set of vertices in and is the set of edges in . The set is called the dominating set in if for every vertex of is adjacent to at least one vertex in . The set is called the total dominating set in graph if for every vertex in is adjacent to at least one vertices in . If is the total domination set with minimum cardinality of the graph and contains another total domination set, for example , then is called the inverse set of total domination respect to . The minimum cardinality of an inverse set of total domination is called the inverse of total domination number which is denoted by .The set of domination and total domination is not singular. A graph that has a total domination set does not necessarily have a inverse total domination set. In this study, exact values are found of , and and,, n is even and , where be a flower graph and T<span style='font-size:10.0pt;mso-ansi-font-siz

The Local Antimagic Total Chromatic Number of Some Wheel-Related Graphs

Let G=(V,E) be a connected graph with |V|=n and |E|=m. A bijection f:V(G)∪E(G)→{1,2,⋯,n+m} is called local antimagic total labeling if, for any two adjacent vertices u and v, ωt(u)≠ωt(v), where ωt(u)=f(u)+∑e∈E(u)f(e), and E(u) is the set of edges incident to u. Thus, any local antimagic total labeling induces a proper coloring of G, where the vertex x in G is assigned the color ωt(x). The local antimagic total chromatic number, denoted by χlat(G), is the minimum number of colors taken over all colorings induced by local antimagic total labelings of G. In this paper, we present the local antimagic total chromatic numbers of some wheel-related graphs, such as the fan graph Fn, the bowknot graph Bn,n, the Dutch windmill graph D4n, the analogous Dutch graph AD4n and the flower graph Fn.

On the resolving strong domination number of some wheel related graphs

This study aims to analyse the resolving strong dominating set. This concept combinations of two notions, they are metric dimension and strong domination set. By a resolving strong domination set, we mean a set D s ⊂ V(G) which satisfies the definition of strong dominating set as well as resolving set. The resolving strong domination number of graph G, denoted by γrst (G), is the minimum cardinality of resolving strong dominating set of G. In this paper, we determine the resolving strong domination number of some wheel related graphs, namely helm graph Hn , gear graph Gn , and flower graph Fln . Through this paper, we will use the notations γst (G) and dim(G) which show the strong domination and dimension numbers.

On r-dynamic vertex coloring of some flower graph families

Let [Formula: see text] be a simple, connected undirected graph with [Formula: see text] vertices and [Formula: see text] edges. Let vertex coloring [Formula: see text] of a graph [Formula: see text] be a mapping [Formula: see text], where [Formula: see text] and it is [Formula: see text]-colorable. Vertex coloring is proper if none of the any two neighboring vertices receives the similar color. An [Formula: see text]-dynamic coloring is a proper coloring such that [Formula: see text] min[Formula: see text], for each [Formula: see text][Formula: see text]. The [Formula: see text]-dynamic chromatic number of a graph [Formula: see text] is the minutest coloring [Formula: see text] of [Formula: see text] which is [Formula: see text]-dynamic k-colorable and denoted by [Formula: see text]. By a simple view, we exhibit that [Formula: see text], howbeit [Formula: see text] cannot be arbitrarily small. Thus, finding the result of [Formula: see text] is useful. This study gave the result of [Formula: see text]-dynamic chromatic number for the central graph, Line graph, Subdivision graph, Line of subdivision graph, Splitting graph and Mycielski graph of the Flower graph [Formula: see text] denoted by [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] respectively.

SSP-Structure of k-Sun Flower, Friendship and Jahangir Graphs

A graph is SSP (Super Strongly Perfect) if all of its (induced) subgraph H in G obsesses a (minimal dominating set) MDS that link up all of its cliques (maximal) in H. It is offered the cyclic structure of k-sun flower graph, friendship and Jahangir graphs and later explored their SSP parameters like counting of colourability, MDS (minimal dominating set) and cliques (maximal) of these graphs.

Some 4-total mean cordial graphs derived from wheel

In this paper we investigate the 4-total mean cordial labeling behaviour of helm, closed helm, flower graph, sunflower graph, gear graph, subdivision of wheel, web graph.

Weakly convex and convex domination numbers for generalized Petersen and flower snark graphs

We consider the weakly convex and convex domination numbers for two classes of graphs: generalized Petersen graphs and flower snark graphs. For a given generalized Petersen graph GP(n, k), we prove that if k = 1 and n ≥ 4 then both the weakly convex domination number γwcon(GP(n, k)) and the convex domination number γcon(GP(n, k)) are equal to n. For k ≥ 2 and n ≥ 13, γwcon(GP(n, k)) = γcon(GP(n, k)) = 2n, which is the order of GP(n, k). Special cases for smaller graphs are solved by the exact method. For a flower snark graph Jn, where n is odd and n ≥ 5, we prove that γwcon(Jn) =2n and γcon(Jn) = 4n.

Standing waves on a flower graph

A flower graph consists of a half line and N symmetric loops connected at a single vertex with N≥2 (it is called the tadpole graph if N=1). We consider positive single-lobe states on the flower graph in the framework of the cubic nonlinear Schrödinger equation. The main novelty of our paper is a rigorous application of the period function for second-order differential equations towards understanding the symmetries and bifurcations of standing waves on metric graphs. We show that the positive single-lobe symmetric state (which is the ground state of energy for small fixed mass) undergoes exactly one bifurcation for larger mass, at which point (N−1) branches of other positive single-lobe states appear: each branch has K larger components and (N−K) smaller components, where 1≤K≤N−1. We show that only the branch with K=1 represents a local minimizer of energy for large fixed mass, however, the ground state of energy is not attained for large fixed mass if N≥2. Analytical results obtained from the period function are illustrated numerically.