Preservation of the Classical Meanness Property of Some Graphs Based on Line Graph Operation

Abstract

In the present paper, we introduce the classical mean labeling of graphs and investigate their related properties. Moreover, it is obtained that the line graph operation preserves the classical meanness property for some standard graphs.

Theoretical framework for a decision support system for micro-enterprise supermarket investment risk assessment using novel picture fuzzy hypersoft graph

“…Balanced Picture Fuzzy Graphs were explored in 2021 by Amanathulla et al [51,52]. Numerous related hybrid fuzzy graph theoretical concepts relating to different aspects of their applications are presented in the following studies [53][54][55][56][57][58].…”

New Perspectives on Classical Meanness of Some Ladder Graphs

“…In addition, more concepts of ladder graphs and related concepts have been studied in [16][17][18][19][20][21][22][23][24]. Recently, Muhiuddin et al have applied various related concepts on graphs in different aspects (see, e.g., [25][26][27][28][29][30][31]).…”

Omega Index of Line and Total Graphs

“…Given a graph G, the line graph L(G) of G is the graph whose vertex set is E(G) with two vertices of L(G) being adjacent iff corresponding edges in G are adjacent. For some applications of the line graph, see, e.g., [4,5]. Similarly, the total graph T(G) of G is the graph whose vertex set is V(G) ∪ E(G) with two vertices of T(G) being adjacent iff the corresponding elements of G are either adjacent or incident.…”

“…Minimal doubly resolving sets and strong metric dimension of the layer sun graph and the line graph of this graph are calculated in [4]. e classical meanness property of some graphs based on line graphs was considered in [5]. For some recent applications of the total graphs, see, e.g., [6][7][8].…”