Rehan-Lanel Indices of Graphs

Abstract

A graph $G$ consists of vertices $V(G)$ and edges $E(G)$. In this paper, we propose four new indices defined and named as first Rehan-Lanel index of $G$ $(RL_1)$, second Rehan-Lanel index of $G$ $(RL_2)$, second Rehan-Lanel index of $G$, third Rehan-Lanel index of $G$, $(RL_3)$ and fourth Rehan-Lanel index of $G$ $(RL_4)$. The degrees of the vertices $u, v \in V(G)$ are denoted by $d_G(u)$ and $d_G(v)$. Based on these new indices and the definitions of Revan degree, Domination degree, Banhatti degree, Temperature of a vertex, KV indices, we subsequently introduced an additional 448 indices/exponentials and computed results for the first four new indices of each subsequent definition, for the standard graphs such as $r-$ regular graph, complete graph, cycle, path and compete bipartite graph. In addition, we performed calculations for the Wheel graph, Sunflower graph, and French Windmill graph. Furthermore, using the exponential of a degree of a vertex, the centrality concept, we introduced another 8 indices. Furthermore, we defined a new degree called Chandana-Lanel degree of a vertex of a graph(CL degree). Using this degree, new 6 indices were defined. Also, we defined the index called the Heronian Rehan-Lanel index using the Heronian mean of two numbers. These novel 462 indices would be advantageous in QSPR/QSAR studies.

Figures (3)

• Figure 1: Wheel Graph
• Figure 2: Sunflower Graph
• Figure 3: French Windmill graph

Theorems & Definitions (109)

• Definition 1
• Proposition 1
• proof
• Corollary 1.1
• Corollary 1.2
• Proposition 2
• proof
• Proposition 3
• proof
• Theorem 1