Path Related Graphs Research Articles

Heptagonal graceful labeling of caterpillar and path related graphs

Heptagonal graceful labeling of caterpillar and path related graphs

L-HILBERT MEAN LABELING OF SOME PATH RELATED GRAPHS

Let be a graph with vertices and edges. The th hilbert number is denoted by and is defined by where A - hilbert mean labeling is an injective function , where that induces a bijection defined by
 for all . A graph which admits such labeling is called a - hilbert mean graph. In this paper, a new type of labeling called - hilbert mean labeling is introduced and the path related graphs is studied.
 AMS Subject Classification – 05C78

A Study on Power-3 Heronian Odd Mean Labeling for some Path Related Graphs

In this article, we discussed Power-3 Heronian odd Mean Labeling for some path related graphs. A function is said to be Power 3 Heronian odd mean labeling of a graph G with q edges, if f is a bijective function from the vertices of G to the set{1,3,5,.......2p-1}such that when each edges uv is assigned the label, then the resulting edge labels are distinct numbers.

Nordhaus-Gaddum Type Relations on Open Support Independence Number of Some Path Related Graphs Under Addition and Multiplication

In this paper, Nordhaus-Gaddum type relations on open support independence number of some derived graphs of path related graphs under addition and multiplication are studied.

Inverse Domination To The Transformation Of Path Related Graphs

A set D of vertices in a graph G (V, E) is a dominating set of G, if every vertex in V-D is adjacent to at least one vertex in D. If V-D contains a dominatingset D’ of G then D’ is called an inverse dominating set with respect to D. In this paper we have established some theorems and properties of the inverse domination number to the transformation of path related graphs.

DETOUR PEBBLING ON PATH RELATED GRAPHS

DETOUR PEBBLING ON PATH RELATED GRAPHS

Extending of Edge Even Graceful Labeling of Graphs to Strong r -Edge Even Graceful Labeling

Edge even graceful labeling of a graph G with p vertices and q edges is a bijective f from the set of edge E G to the set of positive integers 2,4 , … , 2 q such that all the vertex labels f ∗ V G , given by f ∗ u = ∑ u v ∈ E G f u v mod 2 k , where k = max p , q , are pairwise distinct. There are many graphs that do not have edge even graceful labeling, so in this paper, we have extended the definition of edge even graceful labeling to r -edge even graceful labeling and strong r -edge even graceful labeling. We have obtained the necessary conditions for more path-related graphs and cycle-related graphs to be an r -edge even graceful graph. Furthermore, the minimum number r for which the graphs: tortoise graph, double star graph, ladder and diagonal ladder graphs, helm graph, crown graph, sunflower graph, and sunflower planar graph, have an r -edge even graceful labeling was found. Finally, we proved that the even cycle C 2 n has a strong 2 -edge even graceful labeling when n is even.

Differential in infrastructure networks

Let G = (V, E) be a graph of order n and let B(D) be the set of vertices in V \ D that have a neighbor in the vertex set D. The differential of a vertex set D is defined as ∂(D) = |B(D)| − |D| and the maximum value of ∂(D) for any subset D of V is the differential of G. A set D of vertices of a graph G is said to be a dominating set if every vertex in V \ D is adjacent to a vertex in D. G is a dominant differential graph if it contains a ∂-set which is also a dominating set. This paper is devoted to the computation of differential of wheel, cycle and path-related graphs as infrastructure networks. Furthermore, dominant differential wheel, cycle and path-related types of networks are recognized.

Zumkeller labeling of some path related graphs

Zumkeller labeling of some path related graphs

On Mixed Metric Dimension of Some Path Related Graphs

A vertex k ∈ VG determined two elements (vertices or edges) 1, m ∈ VG U EG, if dG(k, 1) =6 dG(k, m). A setRm of vertices in a graph G is a mixed metric generator for G, if two distinct elements (vertices or edges) are determined by some vertex set of Rm. The least number of elements in the vertex set of Rm is known as mixed metric dimension, and denoted as dimm(G). In this article, the mixed metric dimension of some path related graphs is obtained. Those path related graphs are P2n the square of a path, T(Pn) total graph of a path, the middle graph of a path M(Pn), and splitting graph of a path S(Pn). We proved that these families of graphs have constant and unbounded mixed metric dimension, respectively. We further presented an improved result for the metric dimension of the splitting graph of a path S(Pn).

Eccentric domination number of some path related graphs

Eccentric domination number of some path related graphs

Neighbourhood V4–magic labeling of some star and path related graphs

Let V 4 = {0, a, b, c} be the Klein-4-group with identity element 0. A graph G = (V(G), E(G)) with vertex set V(G) and edge set E(G), is said to be Neighbourhood V 4-magic if there exists a labeling f : V(G) → V 4\\{0} such that the sum is a constant map. If this constant is p, where p is any non zero element in V 4 , then we say that f is a p-neighbourhood V 4-magic labeling of G and G is said to be a p-neighbourhood V 4-magic graph. If this constant is 0, then we say that f is a 0-neighbourhood V 4-magic labeling of G and G is said to be a 0-neighbourhood V 4-magic graph. In this paper we study Neighbourhood V 4-magic labeling of some star and path related graphs.

Fuzzy Linear Labeling

A fuzzy linear labeling of a graph is the existence of two injections which assigns values in [0,1]. This labeling fuzzifies the crisp graph. In this paper we show the admissibility of fuzzy linear labeling in some path related graphs.

On SD-Harmonious Labeling

A graph G is said to be SD-harmonious labeling if there exists an injection f: V(G) -> {0,1,2,...,q} such that the induced function f*: E(G) ->{0,2,...,2q-2} defined by f(uv)=S+D (mod 2q) is bijective, where S=f(u)+f(v) and D=|f(u)-f(v)|, for every edge uv in E(G). A graph which admits SD-harmonious labeling is called SD-harmonious graph. In this paper, we investigate SD-harmonious labeling of path related graphs, tree related graphs, star related graphs and disjoint union of graphs.

3-Difference cordial labeling of some path related graphs

<p>Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map where k is an integer 2 ≤ k ≤ p. For each edge uv, assign the label |f(u) − f(v)|. f is called k-difference cordial labeling of G if |vf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x, ef (1) and ef (0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a k-difference cordial labeling is called a k-difference cordial graph. In this paper we investigate 3-difference cordial labeling behavior of triangular snake, alternate triangular snake, alternate quadrilateral snake, irregular triangular snake, irregular quadrilateral snake, double triangular snake, double quadrilateral snake, double alternate triangular snake, and double alternate quadrilateral snake.</p>

On Total Domination in some Path Related Graphs

If G is a graph with vertex set V(G) then dominating set D subset V(G) is called total if every vertex of V(G) is adjacent to at least one vertex of D while it is called equitable if for every vertex u in D there exists a vertex v in V(G) - D such that the degree difference between these vertices is at most one. A dominating set which is both total and equitable is called total equitable dominating set. The minimum cardinality of total dominating set of G is called total domination number of G which is denoted by gamma_t(G). The total equitable domination number of G is the minimum cardinality of total equitable domination number of G which is denoted by gamma_t^e(G). We determine the exact values of total domination number as well as total equitable domination number of some path related graphs.

Hexagonal Difference Prime Labeling of Some Path Graphs

Hexagonal difference prime labeling of vertices of a graph is the labeling of the vertices of the graph with hexagonal numbers and the edges with absolute value of the difference of the labels of the incident vertices. The greatest common incidence number (gcin) of a vertex of degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of degree greater than one is 1, then the graph admits hexagonal difference prime labeling. Here we identify some path related graphs for hexagonal difference prime labeling.

Strong Domination Number of some Path Related Graphs

Let $G =(V, E)$ be a graph and $uv \in E$ be an edge then $u$ strongly dominates $v$ if $deg(u) \geq deg(v)$. A set $S$ is a $strong$ $dominating$ $set$ ($sd-set$) if every vertex $v \in V-S$ is strongly dominated by some $u$ in $S$. We investigate strong domination number of some path related graphs.

Some Path Related 4-Cordial Graphs

In this paper, we discuss 4-cordial labeling of some path related graphs. We prove that middle graph, total graph and splitting graph of the path are 4-cordial. In addition to this we prove that $P_n^2 $ and triangular snakes are 4-cordial.

The B-Chromatic Number of some Graphs

A proper coloring of a graph G is called b-coloring if each color class contains a vertex which is adjacent to at least one vertex of every other color classes. We investigate b-chromatic number of some cycle and path related graphs.