Fixed point of φ-contraction in metric spaces endowed with a graph

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Fixed Points for -Graphic Contractions with Application to Integral Equations (2013, background): “3(2) in [29] are extended to weak ψ-graphic contractive maps defined on a 0-complete partial metric space as follows.”
Fixed point theorems for Reich type contractions on metric spaces with a graph (2012, background): “In [5], the author considered the problem of existence of a fixed point for φ-contractions in metric spaces endowed with a graph.”
Fixed point results for multivalued contractions on a metric space with a graph (2013, background): “Let us mention that different notions of single-valued φ-contractions using comparison functions were introduced and fixed point results were obtained in complete metric spaces endowed with a partial ordering or a directed graph in particular in [1,2,7,11].”