Table 1 Abbreviations of graph terminology.
From: Optimizing hybrid network topologies in communication networks through irregularity strength
S. no. | Graph term | Abbreviation |
|---|---|---|
1 | Cycle graph | \(C_n\) |
2 | Path graph | \(P_n\) |
3 | Vertex set | V(G) |
4 | Edge set | E(G) |
5 | Corona product of cycle with path Graph | \(C_{n}\odot P_m\) |
6 | Dutch windmill graph | \(D_{n}^{m}\) |
7 | Copies of cycle graph | \(C_{p}^{j}\) |
8 | Families of isomorphic cycle subgraphs | \(C_{p}^{j,\Re }\) |
9 | Edge weight of subgraph H | \(wt_{\beta }({\dot{H}})\) |
10 | Vertex weight of subgraph H | \(wt_{\alpha }({\dot{H}})\) |
11 | Total weight of subgraph H | \(wt_{\gamma }({\dot{H}})\) |
12 | Edge H-irregularity strength of Dutch windmill graph by covering with copies of cycle graph | \(\textrm{ehs}(D_{n}^{m}, C_{p}^{j})\) |
13 | Vertex H-irregularity strength of Dutch windmill graph by covering with copies of cycle graph | \(\textrm{vhs}(D_{n}^{m}, C_{p}^{j})\) |
14 | Total H-irregularity strength of Dutch windmill graph by covering with copies of cycle graph | \(\textrm{ths}(D_{n}^{m}, C_{p}^{j})\) |
15 | Edge H-irregularity strength of corona product graph by covering with cycle graph | \(\textrm{ehs}(C_{3}\odot P_m, C_{3})\) |
16 | Vertex H-irregularity strength of corona product graph by covering with cycle graph | \(\textrm{vhs}(C_{3}\odot P_m, C_{3})\) |
17 | Total H-irregularity strength of corona product graph by covering with cycle graph | \(\textrm{ths}(C_{3}\odot P_m, C_{3})\) |
