We introduce new labeling called m-bonacci graceful labeling. A graph G on n edges is if the vertices can be labeled with distinct integers from set {0,1,2,…,Zn,m} such that derived edge labels are first numbers. show complete graphs, bipartite gear triangular grid and wheel graphs not graceful. Almost all trees give to cycles, friendship polygonal snake double graphs.

Core-satellite graphs (sometimes referred to as generalized friendship graphs) are an interesting class of graphs that generalize many well known types of graphs. In this paper we show that two popular clustering measures, the average Watts-Strogatz clustering coefficient and the transitivity index, diverge when the graph size increases. We also show that these graphs are disassortative. In add...

We study infinite graphs in which every set of κ vertices has exactly λ common neighbours. We prove that there exist 2σ such graphs of each infinite order σ if κ is finite and that for κ infinite there are 2λ of them of order λ and none of cardinality greater than λ (assuming the GCH). Further, we show that all a priori admissible chromatic numbers are in fact possible for such graphs.

Nowadays, the problem of finding families graphs for which one may ensure existence a vertex-labeling and/or an edge-labeling based on certain class integers, constitutes challenge researchers in both number and graph theory. In this paper, we focus those vertex-labelings whose induced multiplicative assigns hyper totient numbers to edges graph. way, introduce characterize notions re...

In this paper, we introduce the atom bond connectivity E-Banhatti index and sum of a graph. Also compute these newly defined indices for wheel graphs, friendship chain silicate networks, honeycomb networks nanotubes.

Turán-type problem is one of central problems in extremal graph theory. Erdős et al. [J. Combin. Theory Ser. B 64 (1995) 89-100] obtained the exact Turán number friendship $F_k$ for $n\geq 50k^2$, and characterized all its graphs. Cioabă [Electron. J. 27 (2020) Paper 22] initially introduced Triangle Removal Lemma into a spectral problem, then showed that $SPEX(n, F_k)\subseteq EX(n, F_k)$ $n$ ...

Given a graph F , a graph G is uniquely F -saturated if F is not a subgraph of G and adding any edge of the complement to G completes exactly one copy of F . In this paper we study uniquely Ct-saturated graphs. We prove the following: (1) a graph is uniquely C5-saturated if and only if it is a friendship graph. (2) There are no uniquely C6-saturated graphs or uniquely C7-saturated graphs. (3) F...