Eccentricity splitting graph of a graph

2021 ◽  
pp. 1-12
Author(s):  
Nivedha Baskar ◽  
Tabitha Agnes Mangam ◽  
Mukti Acharya
Keyword(s):  
Splitting Graph

scholarly journals Some New Results on Various Graph Energies of the Splitting Graph

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Zheng-Qing Chu ◽  
Saima Nazeer ◽  
Tariq Javed Zia ◽  
Imran Ahmed ◽  
Sana Shahid
Keyword(s):  
Adjacency Matrix ◽  
Connected Graph ◽  
Absolute Value ◽  
Regular Splitting ◽  
The Absolute ◽  
Splitting Graph ◽  
Simple Connected Graph

The energy of a simple connected graph G is equal to the sum of the absolute value of eigenvalues of the graph G where the eigenvalue of a graph G is the eigenvalue of its adjacency matrix AG. Ultimately, scores of various graph energies have been originated. It has been shown in this paper that the different graph energies of the regular splitting graph S′G is a multiple of corresponding energy of a given graph G.

scholarly journals Domination Integrity of Splitting Graph of Path and Cycle

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Samir K. Vaidya ◽  
Nirang J. Kothari
Keyword(s):  
Connected Graph ◽  
Dominating Set ◽  
Network Expansion ◽  
Splitting Graph ◽  
Two Parameters

If is a dominating set of a connected graph then the domination integrity is the minimum of the sum of two parameters, the number of elements in and the order of the maximum component of . We investigate domination integrity of splitting graph of path and cycle . This work is an effort to relate network expansion and vulnerability parameter.

Splitting on classes of helm graphs and its equitabletotal chromatic number

2020 ◽  
pp. 635-642
Author(s):  
J. Veninstine Vivik ◽  
D. Dafik
Keyword(s):  
Chromatic Number ◽  
Total Coloring ◽  
Total Chromatic Number ◽  
Splitting Graph

The equitable total coloring of a graph $G$ is the different colors used to color all the vertices and edges of $G$, in the order that adjacent vertices and edges are assigned with least different $k$-colors and can be partitioned into colors sets which differ by maximum one. The minimum of $k$-colors required is known as the equitable total chromatic number. In this paper the splitting graph of Helm and Closed Helm graph is constructed and its equitable total chromatic number is acquired.

scholarly journals Vertex Equitable Labeling of Cyclic Snakes and Bistar Graphs

2013 ◽  
Vol 6 (1) ◽  
pp. 79-85 ◽  
Author(s):  
P. Jeyanthi ◽  
A. Maheswari
Keyword(s):  
Splitting Graph ◽  
Square Graph ◽  
Edge Labeling

Let G be a graph with p vertices and q edges and let A = {0, 1, 2,..., }. A vertex labeling f: V (G) ® A induces an edge labeling f * defined by f *(uv) = f(u) + f(v) for all edges uv. For , let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, and the induced edge labels are 1, 2, 3,…, q. In this paper, we establish vertex equitable labeling of square graph of and splitting graph of and kC4 –snake(k?1) and the generalized kCn –snake is vertex equitable if nº0(mod4),n?4.  Keywords: Vertex equitable labeling; Vertex equitable graph.  © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.  doi: http://dx.doi.org/10.3329/jsr.v6i1.15044 J. Sci. Res. 6 (1), 79-85 (2014)  

Hyperbolicity of the cyclic splitting graph

2013 ◽  
Vol 173 (1) ◽  
pp. 271-280 ◽  
Author(s):  
Brian Mann
Keyword(s):  
Splitting Graph

scholarly journals Graph Equations for Line Graphs, Jump Graphs, Middle Graphs, Splitting Graphs And Line Splitting Graphs

2010 ◽  
Vol 9 (2) ◽  
pp. 53-61
Author(s):  
B. Basavanagoud ◽  
Veena Mathad
Keyword(s):  
Line Graph ◽  
Line Graphs ◽  
Line Splitting ◽  
Middle Graph ◽  
Splitting Graph

For a graph G, let G, L(G), J(G) S(G), L,(G) and M(G) denote Complement, Line graph, Jump graph, Splitting graph, Line splitting graph and Middle graph respectively. In this paper, we solve the graph equations L(G) =S(H), M(G) = S(H), L(G) = LS(H), M(G) =LS(H), J(G) = S(H), M(G) = S(H), J(G) = LS(H) and M(G) = LS(G). The equality symbol '=' stands for on isomorphism between two graphs.

scholarly journals Prime labeling of line and splitting graph of brush graph

2021 ◽  
Vol 2106 (1) ◽  
pp. 012030
Author(s):  
F Fran ◽  
D R Putra ◽  
M Pasaribu
Keyword(s):  
Prime Graph ◽  
Bijective Function ◽  
Prime Labeling ◽  
Splitting Graph

Abstract A bijective function f from V(G) to {1,2,…, n} be a prime labeling of a graph G with n order if for every u, v ∈ V(G) such that e = uv ∈ E(G), f(u) and f(v) relatively prime. A prime graph is a graph which admits prime labeling. In this study, we investigate and conclude that the line and splitting graph of the brush graph is a prime graph.

scholarly journals Power domination in splitting and degree splitting graph

2021 ◽  
Vol 40 (6) ◽  
pp. 1641-1655
Author(s):  
J. Anitha ◽  
S. Muthukumar
Keyword(s):  
Dominating Set ◽  
Power Grid ◽  
Domination Number ◽  
Power Domination ◽  
Grid Monitoring ◽  
Vertex Set ◽  
Splitting Graph

A vertex set S is called a power dominating set of a graph G if every vertex within the system is monitored by the set S following a collection of rules for power grid monitoring. The power domination number of G is the order of a minimal power dominating set of G. In this paper, we solve the power domination number for splitting and degree splitting graph.

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