Let G be a graph with p vertices and q edges and an injective function where each is a odd Fibonacci number and the induced edge labeling are defined by and all these edge labeling are distinct is ...called Odd Fibonacci Stolarsky-3 Mean Labeling. A graph which admits a Odd Fibonacci Stolarsky-3 Mean Labeling is called a Odd Fibonacci Stolarsky-3 mean graph.
A set-labeling of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(X)$, where $X$ is a finite set and a set-indexer of $G$ is a set-labeling such that the induced function ...$f^{\oplus}:E(G)\to \mathcal{P}(X)-\{\emptyset\}$ defined by $f^{\oplus}(uv) = f(u){\oplus}f(v)$ for every $uv{\in} E(G)$ is also injective. Let $G$ be a graph and let $X$ be a non-empty set. A set-indexer $f:V(G)\to \mathcal{P}(X)$ is called a topological set-labeling of $G$ if $f(V(G))$ is a topology of $X$. An integer additive set-labeling is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$, whose associated function $f^+:E(G)\to \mathcal{P}(\mathbb{N}_0)$ is defined by $f(uv)=f(u)+f(v), uv\in E(G)$, where $\mathbb{N}_0$ is the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ is its power set. An integer additive set-indexer is an integer additive set-labeling such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. In this paper, we extend the concepts of topological set-labeling of graphs to topological integer additive set-labeling of graphs.
I-CORDIAL LABELING OF SPIDER GRAPHS Sriram, S; Thirusangu, K
TWMS journal of applied and engineering mathematics,
01/2021, Letnik:
11 - Special Issue, Številka:
Jaem Vol 11 - Special Issue, 2021
Journal Article
Recenzirano
Odprti dostop
Let G= (V, E) be a graph with p vertices and q edges. A graph G=(V,E)with p vertices and q edges is said to be an I-cordial labeling of a graph if there exists an injective map f from as p is even or ...odd respectively such 2222 that the injective mapping is defined for f(u) + f(v) ̸= 0 that induces an edge labeling f∗ : E→{0, 1} where f∗(uv) = 1 if f(u) + f(v) > 0 and f∗(uv) = 0 otherwise, such that the number of edges labeled with 1 and the number of edges labeled with 0 differ atmost by 1. If a graph satisfies the condition then graph is called I-Cordial labeling graph or I - Cordial graph. In this paper we intend to prove the spider graph SP(1m,2t) is integer I-cordial labeling graph and obtain some characteristics of I cordial labeling on the graph and we define M-Joins of Spider graph SP(1m,2t) and study their characteristics. Here we use the notation ⌊−p..p⌋∗ = ⌊−p..p⌋ − 0 and ⌊−p..p⌋ = x/x is an integer such that | x |≤ p
Some classes of dispersible dcsl-graphs Jinto, J.; Germina, K.A.; Shaini, P.
Karpats'kì matematinì publìkacìï,
01/2018, Letnik:
9, Številka:
2
Journal Article
Recenzirano
Odprti dostop
A distance compatible set labeling (dcsl) of a connected graph $G$ is an injective set assignment $f : V(G) \rightarrow 2^{X},$ $X$ being a non empty ground set, such that the corresponding induced ...function $f^{\oplus} :E(G) \rightarrow 2^{X}\setminus \{\phi\}$ given by $f^{\oplus}(uv)= f(u)\oplus f(v)$ satisfies $ |f^{\oplus}(uv)| = k_{(u,v)}^{f}d_{G}(u,v) $ for every pair of distinct vertices $u, v \in V(G),$ where $d_{G}(u,v)$ denotes the path distance between $u$ and $v$ and $k_{(u,v)}^{f}$ is a constant, not necessarily an integer, depending on the pair of vertices $u,v$ chosen. $G$ is distance compatible set labeled (dcsl) graph if it admits a dcsl. A dcsl $f$ of a $(p, q)$-graph $G$ is dispersive if the constants of proportionality $k^f_{(u,v)}$ with respect to $f, u \neq v, u, v \in V(G)$ are all distinct and $G$ is dispersible if it admits a dispersive dcsl. In this paper we proved that all paths and graphs with diameter less than or equal to $2$ are dispersible.
A balanced rank distribution labeling of a graph G of order n is a new kind of vertex labeling from {1, 2, 3, ..., k}(n ≤ k ∈ Z+) which leads to a balanced edge labeling of G called edge ranks. In ...this paper, the balanced rank distribution labeling of ladder graphs Ln/2 for even n ≥ 6, complete graphs Kn for n ≥ 3 and complete bipartite graphs Kn/2,n/2 for even n ≥ 4 have been investigated and obtained the results on balanced rank distribution number (brd(G)) for the given graphs as follows: (i) brd(Ln/2)=3n−15,forevenn≥12 (ii) brd(Kn)=n,forn≥3 (iii) brd(Kn/2,n/2) = n, for even n ≥ 4
MMD labeling of W corona with 2m copies of W R, Revathi; D, Angel; D, Iranian ...
2023 Third International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT),
2023-Jan.-5
Conference Proceeding
Consider a graph \hat{\mathrm{G}} consisting of \check{\mathrm{r}} nodes and a relation ƍ from the set of nodes of \hat{\mathrm{G}} to {1,2, ..., ř} so that ƍ satisfies one to one and onto condition. ...Define an edge weight as ƍ (c) ƍ (d)(mod ř) for any edge cd in \hat{\mathrm{G}} . A graph \hat{\mathrm{G}} is a modular multiplicative divisor (MMD) graph if the sum of all edge weights of \hat{\mathrm{G}} is a multiple of \check{\mathrm{r}} . Examine here the role of MMD labeling in the contexture of corona product of wheel W 5 and 2m copies of wheel graph W 5 .
A group valued function on a graph is called balanced if the product of its values along any cycle is equal to the identity element of the group. We compute the number of balanced functions from the ...set of edges and vertices of a directed graph to a finite group considering two cases: when we are allowed to walk against the direction of an edge and when we are not allowed to walk against the edge direction. In the first case it appears that the number of balanced functions on edges and vertices depends on whether or not the graph is bipartite, while in the second case this number depends on the number of strong connected components of the graph.
•We study functions vanishing on each cycle of a directed graph.•The number of such functions depends on whether or not the underlying undirected graph is bipartite.•If every edge is one-way, then the number of such functions depends on the number of strongly connected components.
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