For a graph G, χ(G) (ω(G)) denote its chromatic (clique) number. A P5 is the chordless path on five vertices, and 4-wheel consisting of cycle four vertices C4 plus an additional vertex adjacent to all C4. In this paper, we show that every (P5, 4-wheel)-free G satisfies χ(G)≤32ω(G). Moreover, bound almost tight. That is, there class graphs L such H∈L χ(H)≥107ω(H). This generalizes/improves sever...

The generalization of graceful labeling is termed as -graceful labeling. In this paper it has been shown that , is -graceful for any (set of natural numbers) and some results related to missing numbers for -graceful labeling of cycle , comb , hairy cycle and wheel graph have been discussed.

Let Pn be the path graph on n vertices. In this paper, we consider the distance graphs G(Pn, D), where the distance set D ⊆ {1, 2, 3, . . . , n− 1}. We characterize the distance set D for which G(Pn, D) is one of path, cycle, wheel, regular, bipartite, acyclic, Cr-free, K1,r-free, or having isolated vertices.

A hole in a graph is chordless cycle of length at least 4. theta formed by three internally vertex-disjoint paths 2 between the same pair distinct vertices. wheel and node that has 3 neighbors hole. In this series papers we study class graphs do not contain as an induced subgraph nor wheel. Part II prove decomposition theorem for class, uses clique cutsets 2-joins. paper use to solve several pr...

Our proof (with Robertson and Thomas) of the strong perfect graph conjecture ran to 179 pages of dense matter; and the most impenetrable part was the final 55 pages, on what we called “wheel systems”. In this paper we give a replacement for those 55 pages, much easier and shorter, using “even pairs”. This is based on an approach of Maffray and Trotignon.

In this paper, the weighted Szeged indices of Cartesian product and Corona product of two connected graphs are obtained. Using the results obtained here, the weighted Szeged indices of the hypercube of dimension n, Hamming graph, C4 nanotubes, nanotorus, grid, t−fold bristled, sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.

The injective chromatic number χi(G) [5] of a graph G is the minimum number of colors needed to color the vertices of G such that two vertices with a common neighbor are assigned distinct colors. In this paper we define injective chromatic sum and injective strength of a graph and obtain the injective chromatic sum of complete graph, paths, cycles, wheel graph and complete bipartite graph. We a...

Topological indices are numeric values associated with a graph and characterize its structure. There various topological in theory such as degree-based, distance-based, counting-related indices. Among these indices, degree-based very interesting studied well literature. In this work, we the generalized form of harmonic, geometric-arithmetic, Kulli–Basava power-sum-connectivity index for special...

In this paper, we introduce the E-Banhatti Sombor index and modified their corresponding exponentials of a graph. Also compute these newly defined indices for wheel graphs, friendship tetrameric 1,3-adamantane honeycomb networks. Furthermore, establish some properties index.

Topological indices (molecular descriptors) are numerical values of a chemical structure and represented by graph. Molecular descriptors used in QSPR/QSAR modeling to determine structure’s physical, biological, properties. The cycle graphs symmetric for any number vertices. In this paper, recently defined neighborhood degree sum-based molecular polynomials studied. NM-polynomials some cycle-rel...