Graphs considered in this paper are simple finite undirected graphs without loops or multiple edges. A where each vertex has degree 3 is called cubic graphs. graphs, that is, 1-connected bridge graph traceable if its contains Hamiltonian path otherwise, non-traceable. In paper, we introduce a new family of Non-Traceable Cubic Bridge Graph (NTCBG) satisfy the conjecture Zoeram and Yaqubi (2017)....

We show that every bridgeless cubic graph without a Petersen minor has a nowhere-zero 5-flow. This approximates the known 4-flow conjecture of Tutte. A graph has a nowhere-zero k-flow if its edges can be oriented and assigned nonzero elements of the group Zk so that the sum of the incoming values equals the sum of the outcoming ones for every vertex of the graph. An equivalent definition we get...

A set S of vertices in a graphG is a total dominating set, denoted by TDS, ofG if every vertex ofG is adjacent to some vertex in S (other than itself). The minimum cardinality of a TDS ofG is the total domination number ofG, denoted by t(G). IfG does not contain K1,3 as an induced subgraph, then G is said to be claw-free. It is shown in [D. Archdeacon, J. Ellis-Monaghan, D. Fischer, D. Froncek,...

A bipartite graph is pseudo 2–factor isomorphic if all its 2–factors have the same parity of number of circuits. In a previous paper we have proved that pseudo 2–factor isomorphic k–regular bipartite graphs exist only for k ≤ 3, and partially characterized them. In particular we proved that the only essentially 4–edge-connected pseudo 2–factor isomorphic cubic bipartite graph of girth 4 is K3,3...

In this research article, we present the notion of a cubic planar graph and investigate its related properties. The graphs are more effective than both interval-valued fuzzy as it represents level participation (membership degree) vertices edges in interval form number. Moreover, handles uncertainty vagueness efficiently graph. indicates continuous process, whereas point specific process. We in...

Partial cubes are graphs isometrically embeddable into hypercubes. In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: K2ƒC2n, for some n ≥ 2, generalized Petersen graph G(10, 3), permutahedron, truncated cuboctahedron, or truncated icosidodecahedron. This complete classification of cubic, vertex-transitive partial cubes, a f...